How to solve word problems?

Question

Sumalee and Julia are selling pies for a school fundraiser. Customers can buy cherry pies and lemon meringue pies. Sumaalee sold 1 cherry pie and 14 lemon meringue pies for a total of $206. Julia sold 5 cherry pies and 7 lemon meringue pies for a total of $148. Find the cost of each of one cherry pie and one lemon meringue pie.

Answer 1

Could use substitution method also.

1c+14m=206, so c = 206-14m

5c+7m=148 Substitute for c:

5(206-14m)+7m=148 Remove parentheses.:

1030-70m+7m=148

-63m=-882

m=$14

c=206-14(14)

c=206-196

c=$10

Answer 2

Let c = the cost of one cherry pie.

Let m = the cost of one lemon meringue pie.

1c + 14m = 206

5c + 7m = 148

Multiply the second equation by 2:

10c + 14m = 296

Subtract the first equation from the equation immediately above:

9c = 90

Divide both sides by the coefficient of c:

c = 10

Substitute this value for c back into the very first equation:

(10) + 14m = 206

Subtract 10 from both sides:

14m = 196

Divide both sides by the coefficient of m:

m = 14

Verify these values in the second equation above:

5(10) + 7(14) = 50 + 98 = 148

Checks out!

Cherry pies cost = $10 each.

Lemon meringue pies cost $14 each.