M. Raco grades 7 algebra tests and 10 geometry tests in 227 min He grades 20 algebra tests and 5 geometry tests in 295 min How long does it take to grade each t

Question

Define Variables

Write the 2 equations

Solve

Write the answer in a complete sentence

Answer 1

Let A be the amount of time it takes to complete an Algebra test.

 

Let G be the amount of time it takes to complete a Geometry test.

 

The 2 equations that we can come up with based  the conditions in the problem would be:

 

7A +10G = 227

 

20A+5G = 295

 

multiply the second equation by -2 and and add it to the first one . (Solving a system of equations by elimination)

 

-33A = -363

 

A = 11

 

substitute this value for A in the first equation yielding 

 

10G = 227-77

 

G = 150 / 10

 

= 15

 

It takes 11 minutes to grade an algebra test and 15 minutes to grade  geometry test.