There are 5 times as many oranges as apples, 8 more bananas than apples, and 3 times as many pears as bananas. If the sum of the apples and oranges is equal to the sum of the bananas and pears, then how many of each fruit is there?

x = number of apples

5x = number of oranges {there are 5 times as many oranges as apples}

x + 8 = number of bananas {there are 8 more bananas than apples}

3(x + 8) = number of pears {there are 3 times as many pears as bananas}

x + 5x = x + 8 + 3(x + 8) {sum of apples and oranges equals sum of bananas and pears}

6x = x + 8 + 3x + 24 {combined like terms and used distributive property}

6x = 4x + 32 {combined like terms}

2x = 32 {subtracted 4x from each side}

x = 16 {divided each side by 2}

5x = 80 {substituted 16 for x, into 5x}

x + 8 = 24 {substituted 16 for x, into x + 8}

3(x + 8) = 72 {substituted 16 for x, into 3(x + 8)}

5x = number of oranges {there are 5 times as many oranges as apples}

x + 8 = number of bananas {there are 8 more bananas than apples}

3(x + 8) = number of pears {there are 3 times as many pears as bananas}

x + 5x = x + 8 + 3(x + 8) {sum of apples and oranges equals sum of bananas and pears}

6x = x + 8 + 3x + 24 {combined like terms and used distributive property}

6x = 4x + 32 {combined like terms}

2x = 32 {subtracted 4x from each side}

x = 16 {divided each side by 2}

5x = 80 {substituted 16 for x, into 5x}

x + 8 = 24 {substituted 16 for x, into x + 8}

3(x + 8) = 72 {substituted 16 for x, into 3(x + 8)}

**16 apples, 80 oranges, 24 bananas, and 72 pears****- Algebra House**