SOLUTION: A textbook store sold a combined total of 268 psychology and history textbooks in a week. The number of history textbooks sold was 58 less than the number of psychology textbooks

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Question 1073271: A textbook store sold a combined total of 268 psychology and history textbooks in a week.
The number of history textbooks sold was 58 less than the number of psychology textbooks sold.
How many textbooks of each type were sold?
Answer by Theo(13342) About Me  (Show Source):
You can put this solution on YOUR website!
let x = number of psychology books sold.
let y = number of history books sold.

a total of 368 books were sold.

x + y = 268

the number of history books sold was 58 less than the number of psychology books sold.

y = x - 58

you have 2 equations that need to be solved simultaneously.

they are:

x + y = 268
y = x - 58

since y = x - 58, then replace y in the first equation with x - 58 to get:

x + (x - 58) = 268

remove parentheses to get x + x - 58 = 268.

combine like terms to get 2x - 58 = 268.

add 58 to both sides to get 2x = 326.

divide both sides by 2 to get x = 163.

since x + y = 268, then y = 268 - 163 = 105

the number of psychology books sold is 163.
the number of history books sold is 105.

163 - 105 = 58.

there were 58 less history books sold than psychology books.