SOLUTION: Hi. I have tried solving this, but I am not sure if it's right and would really appreciate your help. A hardware store mixes paints in a ratio of two parts red to six parts yel

Question 174529This question is from textbook Algebra 2
: Hi. I have tried solving this, but I am not sure if it's right and would really appreciate your help.
A hardware store mixes paints in a ratio of two parts red to six parts yellow to make pumpkin orange. A ratio of five parts red to three parts yellow makes red-pepper red. A gallon of pumpkin orange sells for $25, and a gallon of red-pepper red sells for $28.
A. Write a system of equations to model the situation (for this one i wrote
2r+6y=25 and 5r+3y=28, but I dont know if it is correct)
B. Solve the system (I got r=31/8 and y=23/8)
C. Find the cost of 1qt of red paint and the cost of 1qt of yellow paint. Ok, this one I don't know.
I would really appreciate your help. THANKS! This question is from textbook Algebra 2

Answer by josmiceli(19441) (Show Source): You can put this solution on YOUR website!
Let = the cost per gallon of red paint
Let = the cost per gallon of yellow paint
Given is:
A hardware store mixes paints in a ratio of two parts red to six parts yellow to make pumpkin orange.
Therefore, The gallons of red per gallon of punpkin orange is
gal
gal
The gallons of yellow per gallon of pumpkin orange is
gal
gal
Therefore,
(1)
Also given:
A ratio of five parts red to three parts yellow makes red-pepper red.
The gallons of red in a gallon of red-pepper red is
gal
gal
The gallons of yellow in a gallon of red-pepper red is
gal
Therefore,
(2)
(A)
Multiply both sides of (1) by
(1)
Multiply both sides of (2) by
(2)
(B)
Subtract (1) from (2)

Substitute this in (1)

The cost per gallon of red paint is $31
The cost per gallon of yellow paint is $23
(C) There are 4 quarts in a gallon,so
red paint is
/qt
yellow paint is
/qt
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