April, May and June have 90 sweets between them. May has three-quarters of the number of sweets that | MathCelebrity Forum

# April, May and June have 90 sweets between them. May has three-quarters of the number of sweets that

#### math_celebrity

Staff member
April, May and June have 90 sweets between them. May has three-quarters of the number of sweets that June has. April has two-thirds of the number of sweets that May has. How many sweets does June have?

Let the April sweets be a.
Let the May sweets be m.
Let the June sweets be j.

We're given the following equations:
1. m = 3j/4
2. a = 2m/3
3. a + j + m = 90
Cross multiply #2;
3a = 2m

Dividing each side by 2, we get;
m = 3a/2

Since m = 3j/4 from equation #1, we have:
3j/4 = 3a/2

Cross multiply:
6j = 12a

Divide each side by 12:
a = j/2

So we have:
1. m = 3j/4
2. a = j/2
3. a + j + m = 90
Now substitute equation 1 and 2 into equation 3:
j/2 + j + 3j/4 = 90

Multiply each side by 4 to eliminate fractions:
2j + 4j + 3j = 360

To solve this equation for j, we type it in our search engine and we get:
j = 40

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