Chapter 3.6, Problem 41PPSE

Solution

Tocalculate:The cost of 1 quart of red paint and the cost of 1 quart of yellow paint if hardware store mixes paints in a ratio of two parts red to six parts yellow to make two gallons of pumpkin orange. A ratio of five parts red to three parts yellow makes two gallons of pepper red. A gallon of pumpkin orange sells for $25 and a gallon of pepper red sells for $28.

The cost of 1 quart of red paint is $7.75 and 1 quart of yellow paint costs $5.75.

Given information:

It is given that hardware store mixes paints in a ratio of two parts red to six parts yellow to make two gallons of pumpkin orange. A ratio of five parts red to three parts yellow makes two gallons of pepper red. A gallon of pumpkin orange sells for $25 and a gallon of pepper red sells for $28.

Formula used:

  $1gallon=4quarts$

Calculation:

Consider the given information.

Let x is the cost of 1 quart of red paint and cost of 1 quart of yellow paint is represented by y .

It is given that two gallons of pumpkin orange contains 2 part of red paint and 6 part of yellow paint and a gallon of pumpkin orange sells for $25 so two gallons of pumpkin orange cost $50.

Thus, 2 part of red paint and 6 parts of yellow paint sold $50.

  $\begin{array}{c}2x+6y=50\\ x+3y=25\end{array}$

Also, two gallons of pepper red contains 5 parts of red and 3 parts of yellow paint.

One gallon of pepper red costs $28 so the cost of two gallons will be $56.

Therefore 5 part of red paint and 3 parts of yellow paint sold for $56. This can be written as: $5x+3y=56$

Write it into matrix form.

  $\left[\begin{array}{ccc}1& 3& 25\\ 5& 3& 56\end{array}\right]$

Now use Calculator to solve the equation.

Step 1: Press the 2ND key then press MATRX and select EDIT.

Step 2: Click 1 to access matrix A.

Step 3: Input the dimensions and enter the entries by pressing ENTER after each value.

  

Step 4: Press 2ND QUIT 2ND MATRX and select MATH.

Step 5: Click ALPHA B 2ND MATRX 1 ) .

  

Step 6: Now press ENTER.

  

The cost of 1 quart of red paint is $7.75 and 1 quart of yellow paint costs $5.75.