SOLUTION: Question1
a) the length of rectangle is 1 cm less than 3 times the width, if the perimeter is 54 cm, find the dimentions of a rectangle.
b) 400 tickets were sold for a s
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Question 106548: Question1
a) the length of rectangle is 1 cm less than 3 times the width, if the perimeter is 54 cm, find the dimentions of a rectangle.
b) 400 tickets were sold for a school play, General admission tickets were $4 while student tickets were $3, if the total tickets sales were $1350, how many of each type of ticket were sold?
c) How much pure alcohol must be added to 9 quarts of water to obtain a mixture of 40% alcohol?
d) On Friday morning, Ali drove from his house to the beach in 4hrs, in coming back on Sunday afternoon, heavy traffics slowed his speed by 10mi/hrs, and the trip took 5 hrs, what was his average speed in each direction?
Thank you in advance
Answer by ankor@dixie-net.com(22740) (Show Source): You can put this solution on YOUR website!
a) the length of rectangle is 1 cm less than 3 times the width, if the perimeter is 54 cm, find the dimensions of a rectangle.
:
Just write an equation for what it says:
"the length of rectangle is 1 cm less than 3 times the width,"
L = 3W - 1
:
"the perimeter is 54 cm,"
2L + 2W = 54
Substitute (3W-1) for L (from the 1st statement)
2(3W-1) + 2W = 54
Find W
6W - 2 + 2W = 54
8W = 54 + 2
8W = 56
W = 56/8
W = 7
I'll let you find L using the 1st statement equation
:
:
b) 400 tickets were sold for a school play, General admission tickets were $4 while student tickets were $3, if the total tickets sales were $1350, how many of each type of ticket were sold?
:
Let x = no. of general admission tickets; let y = no. of student tickets
:
Write an equation for each statement:
"400 tickets were sold for a school play,"
x + y = 400
y = 400 - x; we can use this for substitution
:
"General admission tickets were $4 while student tickets were $3, the total tickets sales were $1350,"
4x + 3y = $1350
Substitute (400-x) for y in the above equation, find x:
4x + 3(400-x) = 1350
4x + 1200 - 3x = 1350
4x - 3x = 1350 - 1200
x = 150 general admission tickets
Here again I will let you find y from the 1st statement equation
Check your solution in the $$ equation
:
:
c) How much pure alcohol must be added to 9 quarts of water to obtain a mixture of 40% alcohol?
:
Let x = amt of alcohol required
A simple equation will do this:
x = .40(x+9)
x = .4x + 3.6
x - .4x = 3.6
.6x = 3.6
x = 3.6/.6
x = 6 quarts of alcohol required
:
:
d) On Friday morning, Ali drove from his house to the beach in 4 hrs, in coming back on Sunday afternoon, heavy traffics slowed his speed by 10mi/hrs, and the trip took 5 hrs, what was his average speed in each direction?
:
Let s = his speed to the beach
then
(s-10) = his speed back
:
The distance there and back are the same, so write a distance equation
Distance = time * speed
:
return dist = to beach dist
5(s-10) = 4s
5s - 50 = 4s
5s - 4s = +50
s = 50 mph to the beach
:
I'll let you provide the speed on the return trip
:
Did this help you get a handle on this stuff? Hope so.
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