Write a system of equations to represent the situation and solve. Define your variables.

Question

A basket of cupcakes and cookies contains 12 desserts. Cupcakes cost $3 each, and cookies cost $2 each. The basket costs $32. Write and solve a system of linear equations to find the number of cupcakes and cookies. Show you work.

Answer 1

x for cupcakes  ; y for cookies

 

x + y = 12 ----> translation of the first sentence.

 

3x + 2y = 32 --> combined translation of the second and third sentences.

 

Line 2 multiplied by 3 minus line 3 eliminates x !

 

y = 36 - 32 = 4 and x = 8 after substitution in line 2.