the cost of 8 muffins and 2 quarts of milk is 18 dollars. The cost of 3 muffins and one quart of milk is 7.50 dollars. write a system of equations and solve.

Question

i cant find out how to show my work to get the right answer.

Answer 1

Let M = cost of 1 muffin

Let Q = cost of 1 quart of milk

 

then the cost equations are:

 

#1   8M + 2Q = $18 

#2   3M + 1Q = $7.50

 

We can solve two ways.

1) use one eqn to solve for one variable in terms of the other, then substitute into the other eqn.

2) Use row operations to eliminate on variable (M or Q) to solve for one variable, then substitute it's value in either equation for the other variable. 

 

Using method 2, we can multiply eqn. #2 by 2, and subtract from equation #1.

 

2 [3M + 1Q = $7.50]  =  6M + 2Q = $15.00     (eqn #2  mult by 2)

 

8M + 2Q = $18.00

6M + 2Q = $15.00        (subtract from eqn 1)

============

2M + 0 = $3.00            or  M = $1.50    (now substitute M in either eqn for Q. I'll use #2 again)

 

3(1.50) + Q = $7.50

 

Q = 7.50 - 4.50   OR  Q = $3.00 

 

SO,    M (1 muffin) = $1.50   Q(quart of milk) = $3.00 

 

you can verify that these costs satisfy both eqn 1 and 2.