Question 174529
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/(2 + 6)}}}gal
{{{1/4}}}gal
The gallons of yellow per gallon of pumpkin orange is
{{{6/(2 + 6)}}}gal
{{{3/4}}}gal
Therefore,
(1) {{{(1/4)r + (3/4)y = 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/(3 + 5)}}}gal
{{{5/8}}}gal
The gallons of yellow in a gallon of red-pepper red is
{{{3/8}}}gal
Therefore,
(2) {{{(5/8)r + (3/8)y = 28}}}
(A)
Multiply both sides of (1) by {{{4}}}
(1) {{{r + 3y = 100}}}
Multiply both sides of (2) by {{{8}}}
(2) {{{5r + 3y = 224}}}
(B)
Subtract (1) from (2)
{{{4r = 124}}}
{{{r = 31}}}
Substitute this in (1)
{{{31 + 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
{{{31/4 = 7.75}}}/qt
yellow paint is
{{{23/4 = 5.75}}}/qt