How can the number 39 be divided into two parts in order that the sum of 2/3 of one part and 3/4 of the other part is 28? Explain your workings

Let x be one part and 39-x be the other part.

ans:2/3(x)+3/4(39-x)=28
x=15

therefore,one part divided out is 15 and the other part is (15-2)=13

oh sorry,the other part is 39-15 and should be24

Mary's age is 2/3 that of Peter's. Two years ago Mary's age was 1/2 of what Peter's age will be in five years time. How old is Peter now?

2/3

To solve this problem, we need to set up an equation based on the information given. Let's assume that the first part of the number we're trying to find is represented by "x," and the second part is represented by "39 - x."

According to the problem, the sum of 2/3 of the first part and 3/4 of the second part is 28. Mathematically, this can be expressed as:

(2/3) * x + (3/4) * (39 - x) = 28

To solve this equation, we need to simplify it and isolate x.

First, multiply 2/3 with x:

(2/3) * x + (3/4) * (39 - x) = 28
(2/3) * x + (3/4) * 39 - (3/4) * x = 28

Next, simplify the equation by multiplying:

(2/3) * x + (117/4) - (3/4) * x = 28

Now, combine the x terms and the constant terms:

(2/3 - 3/4) * x + (117/4) = 28
[(8 - 9)/12] * x + (117/4) = 28

Simplify the numerator:

(-1/12) * x + (117/4) = 28

Next, isolate the variable by subtracting (117/4) from both sides:

(-1/12) * x = 28 - (117/4)

To simplify the right side of the equation, we need to find a common denominator for 28 and (117/4):

(-1/12) * x = (112/4) - (117/4)
(-1/12) * x = (-5/4)

Now, multiply both sides of the equation by -12 to get rid of the fraction:

x = (-5/4) * (-12)

Simplify the right side:

x = 15

Now that we know one part is 15, we can find the other part by subtracting it from 39:

39 - x = 39 - 15 = 24

So, the two parts are 15 and 24.