Question 572055: Please, could you help me with these problems?
1. The perimeter of a triangle is 52centimeters. Find the length of its sides, if the longest side is 5 cm longer that the shortest side and the remaining side is 2 centimeters longer that the shortest.
3. David has $15.000 to invest. He invest 10000 in a mutual found that pays 12% annuak simple intrest. if he wants to make at lest 2200 in yearly interest at what minimum rate does the remainder of the money need to be invested?
2. The difference of triple number and 1/2 is equal to the sum of the number and 2/3 . find the number
Thank you so much for your help
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! 1. The perimeter of a triangle is 52centimeters. Find the length of its sides, if the longest side is 5 cm longer that the shortest side and the remaining side is 2 centimeters longer that the shortest.
let the sides of the triangle be a, b, and c.
a is the longest side.
c is the shortest side.
a = c+5
b = c+2
perimeter is equal to a + b + c
since a = c+5 and b = c+2, this equation becomes:
perimeter is equal to c+5 + c+2 + c which becomes:
perimeter is equal to 3c+7
since perimeter is equal to 52 cm, this means that:
3c+7 = 52
subtract 7 from both sides of this equation to get:
3c = 45
divide both sides of this equation by 3 to get:
c = 15
this means that:
c = 15
c+2 = 17
c+5 = 20
this means that:
perimeter equals 15 + 17 + 20 which is equal to 52 cm.
that's your answer.
length of the sides of the triangle are:
15, 17, 20
3. David has $15,000 to invest. He invest 10,000 in a mutual found that pays 12% annual simple interest. if he wants to make at lest 2,200 in yearly interest at what minimum rate does the remainder of the money need to be invested?
the interest he makes on 10,000 at 12% interest equals $1,200.
he needs as least $1,000 more interest from the remaining $5,000 to achieve his goal.
let x equal the interest rate he needs.
$5,000*x = $1,000
divide both sides of this equation by $5,000 to get:
x = $1,000 / $5,000 = 1/5 = .20 which is equal to 20%.
he needs 20% interest on the $5,000 to achieve his goal.
if he gets that, then his total interest at the end of the year will be:
$10,000 * .12 + $5,000 * .2 = $1,200 + $1,000 = $2,200.
your answer is that he needs 20% interest on the remaining $5,000 to achieve his goal of $2,200 as the minimum interest he needs to earn.
2. The difference of triple number and 1/2 is equal to the sum of the number and 2/3 . find the number
let x be the number.
the difference of triple the number and 1/2 is equal to 3x - 1/2.
the sum of the number and 2/3 is equal to x + 2/3
the statement of:
The difference of triple number and 1/2 is equal to the sum of the number and 2/3 is equivalent to the equation of:
3x - 1/2 = x + 2/3
subtract x from both sides of this equation to get:
2x - 1/2 = 2/3
add 1/2 to both sides of this equation to get:
2x = 2/3 + 1/2 which is equivalent to:
2x = 4/6 + 3/6 which simplifies to:
2x = 7/6
divide both sides of this equation by 2 to get:
x = 7/12.
assuming x = 7/12, the original statement says:
The difference of triple number and 1/2 is equal to the sum of the number and 2/3.
triple the number is 21/12.
subtracting 1/2 from 21/12 gets you 21/12 - 6/12 = 15/12. *****
adding 2/3 to the original number gets you:
7/12 + 2/3 = 7/12 + 8/12 which becomes 15/12 *****
since they're both equal to 15/12 then they are equal to each other which satisfies the original problem statement of:
The difference of triple number and 1/2 is equal to the sum of the number and 2/3.
your answer is:
x = 7/12.
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