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

Algebra ->  Matrices-and-determiminant -> 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      Log On


   

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) About Me  (Show Source):
You can put this solution on YOUR website!
Let r = the cost per gallon of red paint
Let y = 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
2%2F%282+%2B+6%29gal
1%2F4gal
The gallons of yellow per gallon of pumpkin orange is
6%2F%282+%2B+6%29gal
3%2F4gal
Therefore,
(1) %281%2F4%29r+%2B+%283%2F4%29y+=+25
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
5%2F%283+%2B+5%29gal
5%2F8gal
The gallons of yellow in a gallon of red-pepper red is
3%2F8gal
Therefore,
(2) %285%2F8%29r+%2B+%283%2F8%29y+=+28
(A)
Multiply both sides of (1) by 4
(1) r+%2B+3y+=+100
Multiply both sides of (2) by 8
(2) 5r+%2B+3y+=+224
(B)
Subtract (1) from (2)
4r+=+124
r+=+31
Substitute this in (1)
31+%2B+3y+=+100
3y+=+69
y+=+23
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
31%2F4+=+7.75/qt
yellow paint is
23%2F4+=+5.75/qt