Algebra Homework help

Question

A textbook store sold a combined total of 321

 psychology and math textbooks in a week. The number of math textbooks sold was 75

 less than the number of psychology textbooks sold. How many textbooks of each type were sold?

Answer 1

The word problem simplifies to:

321 = m +p and m = p +75; where m=math textbooks and p=psychology textbooks

This is a system of equations problem with 3 ways to solve it, but the simplest way is through substitution and elimination.

We will use substitution, because we already have a value: m.

Our new equation is 321=p +75 +p

Combine like terms: 321= 2p +75

Move the 75: 321-75= 2p +75 -75

Simplify: 246= 2p

Get p by itself: 246/2 = 2p/2

Simplify: 123 = p; We now have p.

Now we can replace the p in either equation with 123.

For simplicity, we will use the equation for the math textbooks: m = p + 75

m = 123 +75

Simplify: m = 198

We now have both the variable values: p = 123 and m = 198

Check your answers for accuracy by placing both in the original 321 = m +p: 321 = 123 + 198

Simplify: 321 = 321

This answer checks.