Answer:
[tex]Dina= 35[/tex]
Step-by-step explanation:
Given
[tex]Ratio = 4:2:5[/tex]
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
[tex]Peter: Chris: Dina = 4:2:5[/tex]
Considering Peter and Chris
[tex]Peter: Chris = 4:2[/tex]
Let the number of Chris' A's be represented by A
This implies that:
Peter's = 14 + A
And as such;
[tex]14 + A : A = 4 : 2[/tex]
Convert ratio to division
[tex]\frac{14 + A}{ A} = \frac{4}{ 2}[/tex]
Multiply both sides by A
[tex]A * \frac{14 + A}{ A} = \frac{4}{ 2}* A[/tex]
[tex]14 + A = \frac{4}{ 2}* A[/tex]
[tex]14 + A = 2* A[/tex]
[tex]14 + A = 2 A[/tex]
Subtract A from both sides
[tex]14 + A-A = 2 A-A[/tex]
[tex]14 = A[/tex]
This means that;
Chris answered 14 while Pete answered 28 (14 + 14)
Considering Chris and Dana
[tex]Chris :Dana = 2:5[/tex]
Replace Chris with 14
[tex]14:Dana = 2:5[/tex]
Convert ratio to division
[tex]\frac{14}{ Dina} = \frac{2}{5}[/tex]
Cross Multiplication
[tex]Dina * 2 = 14 * 5[/tex]
Divide both sides by 2
[tex]\frac{Dina * 2}{2} = \frac{14 * 5}{2}[/tex]
[tex]Dina= \frac{14 * 5}{2}[/tex]
[tex]Dina= \frac{70}{2}[/tex]
[tex]Dina= 35[/tex]
Hence, Dina had 35 A's
