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

Answer:

$Dina= 35$

Step-by-step 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

$\frac{14 + A}{ A} = \frac{4}{ 2}$

Multiply both sides by A

$A * \frac{14 + A}{ A} = \frac{4}{ 2}* A$

$14 + A = \frac{4}{ 2}* A$

$14 + A = 2* A$

$14 + A = 2 A$

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

$\frac{14}{ Dina} = \frac{2}{5}$

Cross Multiplication

$Dina * 2 = 14 * 5$

Divide both sides by 2

$\frac{Dina * 2}{2} = \frac{14 * 5}{2}$

$Dina= \frac{14 * 5}{2}$

$Dina= \frac{70}{2}$

$Dina= 35$

Hence, Dina had 35 A's