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Perimeter of the rectangle = 2L+2B
L=B+50
half the perimeter of a rectangular lot, which is 50 feet longer than it is wide, is 350 feet
So,
.5*(2* (B+50))+(2B))= 350
4B+100=700
solving for B we get, B as 150 feet
And L= 150+50
=200 feet

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1)The PTA at Magnolia Elementary is selling spirit shirts for students to wear on Fridays to raise money for a new track field. For any orders of 100 or more, the silk screening company will charge $195 set up fee and $3.50 per
T-shirt ordered. The PTA is charging $5 per shirt to students.
a. Write an equation for the total cost, C, of ordering t T-shirts. b. b. Write an equation for the revenue, R, for selling t T-shirts.
c. Write an equation for the profit, P, made by the PTA for selling the shirts.
d. (1 point) How many shirts does the PTA have to sell before they start making money for their fundraiser?
e. (1 point) If the PTA needs to raise $5000 for the new track field, how many T-shirts do they need to sell?
Ans:
Consider fixed cost(FC)= 195$
Cost pice = 3.50$
Selling price = 5$
a.total cost = t*3.50 + 195
Where t= no of shirts ordered .
total cost and fixed cost .The above question is answered on the basis that all the expense includes FC+Variable cost
Where variable cost here is cost of one shirt *total ordered.
b.Revenue= t*5$
where t= toal shirts ordered.
c.P = revenue - Total cost
=(t*5)-(t*3.50 + 195)
d.this is calculated by using break even point, in that point there will be no profit and no loss, after this poin, the company faces profit.
break even quantity = FC/(CP-SP per unit)
=195/(5-3.5)
=130 shirts.
So this company have to sell 130 shirts to make a profit.
e.use this formula P = Total revenue - total cost
5000= (X*5)-(X*3.50 + 195)
Where X is the total number of shirts to be sold to attain a profit of 5000$
Solving for X we get 3203 (rounded for nearest whole number)i.e., number of shirts to be sold.

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just express all the students of the particular grade as a fraction of the total students:
A's %=(5/15)=.33
B's %=(4/15)=.27
C's %=(6/15) =.4
i.e., 33%, 27% , 40% respectively...

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The sum of the ages of a father and his son is 56 years.Seven years ago the father was five times as old as his son.Find the age of the father now.
Ans:
take 7 years back,
Son=X
Dad= 5X
Now,The age of the son = X+7
The age of the dad = 5X+7
As, sum of the ages of a father and his son is 56 years
(X+7)+(5X+7)=56
6X+14=56
6X = 42
X=7
Dad age, 7*5=35 i.e., 7years back.
So the age of the father now is 35+7= 42 years

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7x-5x+15=x+8
Bring X one side and constants to the other side..
So if you rearrange
7x-5x-x= 8-15
x= -7

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60 cans takes 1$---------------- 1
so X cans takes 5000$------------ 2
Cross multiply the above two eqns
60*5000 = X cans
so, total cans = 300,000

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one number is 12 more than another.the larger is 7 times smaller.what are the numbers?
ans:
let one no be X
and anothr no be y
one number is 12 more than another : so X = Y +12----- (1)
the larger is 7 times smaller : SO X = 7*Y ---- (2)
SUBS 2 IN 1 , YO WILL GET THE ANSW....

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number of ways in which 6 men and 5 women can dine at a round table if no 2 women are to sit together is given by?
sol :
x is the position of the men
y is the position of the women
yxyxyxyxyxyxy
in the above pattern with 6 man ,in 7 positions the 5 women can be placed
so total ways = 7c5 = 42 ways

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1.IF THE SUM OF TEN CONSECUTIVE POSITIVE INTEGERS IS 115, FIND THE LARGEST OF THESE INTEGERS.
sol :
let the nos be x , x+1, x+2, x+3, x+4, x+5, x+6, x+7, x+8, x+9
so 10x + 45 = 115
solve tis you will get x = 7
substitute in the 10th number = x + 9
largest no = 16
2.THREE CONSECUTIVE INTEGERS HAVE A SUM OF 12 AND A PRODUCT OF 60. IF THE SMALLEST INTEGER IS 3 FIND THE LARGEST NUMBER.
sol :
if first no is 3 so ,the third consecutive number is 3 + 2 = 5 , which is the largest.

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A fast food chain offers a special menu for children for which there is a choice of a hamburger or a chicken sandwich with either french fries or a salad, plus one of six beverages. How many special menu possibilities are there?
sol:
( 1 from hamb or sandwich * 1 from french fries or salad * 1 from 6) = total ways
2c1 * 2c1 * 6c1 = 24 ways
verify this answer with your friends..

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the coat of 3 large candles and 5 small is 6.40. the cost of 4 large candles and 6 small candles is 7.50 which pair of equation can be used to determine, t, the cost of a large candle and s, the cost of a small candle.
sol:
let t,be the cost of a large candle and s,be the cost of a small candle.
3t + 5s = 6.40--------1
4t + 6s = 7.50--------2
the above two equations help in finding t & s

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In 5 years, Alessandro will eb three times as old as Frederico will be then. The sum of their ages now is 86. How old will each of them be in 3 years?
sol:
let ales age = x
fred age = y
in 5 years,
(x+5) = 3(y+5)---------- 1
present;
x + y = 86 ---------- 2
solve 1 & 2 as equations which gives x = 67 , y = 19
so after 3 years , x = 70 , y = 22

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Marcella traveled for 45 minutes at an average rate of 40 miles per hour. How far did Marcella travel?
sol:
distance = speed * time
=40 * 3/4 (3/4 = 45/60 --- converting to hours)
= 30 miles

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How many gallons of hydrochloric acid must be added to 12 gallons of a 30% solution to obtain a 40% solution?
sol:
x be the extra added solution
30% of 12 gallons = 3.6 gall.
so forming the equation :
( 3.6 + x)/(12+x) = 40 / 100
solve for x you will get the required quantity which is 2 gallons

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The bookstore sold 348 notebooks the first day of classes, some at $2.85 each and the rest at $3.95 each. The total amount taken in was $1154.60. How many of each kind of notebook were sold?
sol:
let x be one kind of note book
348 - x be the other kind of notebook
as given : (2.85 * x) + ((348 - x) * 3.95) = 1154.60
here solve for x you will get x = 200 & the other kind notebook as 148

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Suppose a dice is tossed.What is the probabilitythat at most one 6 appears.
sol:
here S = (1,2,3,4,5,6)
E be the event of getting 6
P(E) = N(E)/N(S)
= 1/6

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Five girls and five boys are getting together for a party.Suppose one of the boys has 2 sisters amoung the five girls, and he would not accept either of them as a partner.How many couples can be formed
sol :
i gues this will be the solution do check the answer with your friends ...
(1 from 5 boys) * (1 from 3 girls ) = total ways
5c1 * 3c1 = 15 ways

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eight times the larger of two numbers decreased by three times the smaller is 148. nine times the smaller decreased by twenty is equal to eight times the larger. find the two numbers
sol :
forming the equation with the given datas :
let x be the larger number and y be the smaller number
so as given 8x - 3y = 148 ------(1)
9y - 20 = 8x ----------(2)
solve the anove two equation for x & y ,you will get the required nos ,where x = 29 , y = 28.

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charels is twice as old as william.Four years ago Charles was 3 times as old as
william.How old is each now?
sol:
let william's age = x
charle's age = 2x ,as given
forming the equation with the data they gave,
2x - 4 = 3(x - 4)
solve for x you will get william's = 8 years
charle's = 16 years

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a train leaves Philadelphia for Atlanta at 12 noon, traveling 70 mph. another train leaves Atlanta for Philadelphia at 2pm traveling 60 mph. The distance from Philadelphia to Atlanta is 400 miles. Where d the trains meet? When do they meet?
sol :
suppose they meet x hrs after 12. then
dist moved by first in x hrs + dist moved by second in (x - 1) hrs = 400
70 x + 60(x-2) = 400
solving for x you come to know 4 hrs after the 12.

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A motorboat heads upstream on a river that has a current of 3 miles per hour. The trip upstream takes 5 hours, and the return trip takes 2.5 hours. What is th speed of the motorboat?
let the speed of the boat = x
speed of boat in upstream = x - 3
speed of boat in downstream = x + 3
distance = speed * time
so (x - 3)* 5 = (x + 3) * 2.5
solve for x to get the speed of the boat .

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A club offers single memberships, couple memberships, and family memberships. The club has sold a total of 1530 memberships. The couple memberships are 38 more than twice the single memberships. The family memberships are 8 less than three times the single ones
sol :
as given : s + c + f = 1530 ----(1)
c = 38 +2s ---------(2)
f = 3s - 8 ---------(3)substituting 2& 3in equation 1 you can get the required value which gives s =300 , f = 892 , c = 338

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Seven students applied for a position on the four-member student review board. In how many ways could four students have been selected for the board?
sol :
(4 from 7)
so total ways = 7c4 =(7*6*5*4)/(4*3*2*1) = 35 ways

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In how many ways can we select a class president from a group of 4 scholars, a secretary from a group of 3 girls and an adviser from a group of 3 professors?
sol :
(1 from 4) * (1 from 3) * (1 from 3)
so 4c1 * 3c1 * 3c1 = 36 ways

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what is the largest circle which can be drawn from a square sheet with a side of 81cm? which area is greater, the circle or the square sheet?
sol :
the largest circle drawn in a square is by taking the diagonal as diameter of the circle .
now about circle, its dia = sq.root of(81^2 + 81^2) =114.5 cm
area = pi * r^2 = pi *(114.5/2)^2.-------- (1)
area of square = 81^2 -------- (2)
compare the answer of 1 & 2 you will get the answer.

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Justin can invite 2 of his 6 friends to go to the football game with him. How many combinations of 2 friends can Justin take to the game?
sol :
2 ppl from 6
so 6c2 = 15 ways

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The height of a rectangle is half as long as its base.If its height is increased by 5 and its base is decreased by 2, its perimeter is equal to 60. Find the height and base of the rectangle.
sol:
let height = b
base = l
as given :
b = (1/2) * l -------- (1)
2 * ((b + 5) + (l - 2)) = 60--------(2)
equation 2 gives l + b =27 -----(3)
substitute 1 in 3 and simplify to get the required values

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Three times one number minus a second is 8, and the sum of the number is 12. Find the numbers.
sol:
let x = one number
y = other number
form the equations to find x and y
(3 * x) - y = 8 ---------(1)
x + y = 12----------(2)
solve 1 & 2 ,you will get the required nos.

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A student earns $10 an hour for the first 40 hours she works in a week and $15 an hour for every hour after that (overtime). Each week she has $125 deducuted from her check for imcome takes and retirement. If she works 47 hours in a week, how much is her take-home pay?
sol:
forming equations using given data:
she works for 47 hours
so , AS GIVEN :
(10 * 40) + (15 * 7) - 125 = take home pay
solving above expression will give you the answer.

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what is the area of a square with a side length of 4 inches
sol :
let x be the side of the square.
area of square = x^2 sq. units
substitute 4 in the place of x
solve you will get the answer.

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x^3-64
sol :
x ^ 3 = 64
x * x * x = 64
so 4 will come in the place of x.