Question

Pete, Chris, and Dina realized that the number of A’s they each received on their report cards were in a ratio of 4:2:5. If Pete got 14 more A’s than Chris, how many A’s did Dina get?

Answer 1

`Dina= 35`

Explanation:

Given

`Ratio = 4:2:5`

Peter = 14 more A's than Chris

Required

How many A’s did Dina get?

The order of the ratio is Peter: Chris: Dina

This implies that

`Peter: Chris: Dina = 4:2:5`

Considering Peter and Chris

`Peter: Chris = 4:2`

Let the number of Chris' A's be represented by A

This implies that:

Peter's = 14 + A

And as such;

`14 + A : A = 4 : 2`

Convert ratio to division

`(14 + A)/( A) = (4)/( 2)`

Multiply both sides by A

`A * (14 + A)/( A) = (4)/( 2)* A`

`14 + A = (4)/( 2)* A`

`14 + A = 2* A`

`14 + A = 2 A`

Subtract A from both sides

`14 + A-A = 2 A-A`

`14 = A`

This means that;

Chris answered 14 while Pete answered 28 (14 + 14)

Considering Chris and Dana

`Chris :Dana = 2:5`

Replace Chris with 14

`14:Dana = 2:5`

Convert ratio to division

`(14)/( Dina) = (2)/(5)`

Cross Multiplication

`Dina * 2 = 14 * 5`

Divide both sides by 2

`(Dina * 2)/(2) = (14 * 5)/(2)`

`Dina= (14 * 5)/(2)`

`Dina= (70)/(2)`

`Dina= 35`

Hence, Dina had 35 A's