a textbook store sold a combined total of 367...
a textbook store sold a combined total of 367 sociology and psychology textbooks in a week. the number of psychology textbooks sold was 55 less than the number of sociology textbooks sold. how many textbooks of each type were sold?\nnumber of sociology textbooks sold:\nnumber of psychology textbooks sold:
Answer
# Explanation:
## Step1: Let variables
Let $x$ be the number of sociology textbooks sold and $y$ be the number of psychology textbooks sold. We know that $x + y=367$ and $y=x - 55$.
## Step2: Substitute $y$ into the first - equation
Substitute $y=x - 55$ into $x + y=367$, we get $x+(x - 55)=367$.
## Step3: Simplify the equation
Expand the left - hand side: $x+x - 55=367$, which simplifies to $2x-55 = 367$.
## Step4: Solve for $x$
Add 55 to both sides of the equation: $2x=367 + 55=422$. Then divide both sides by 2: $x=\frac{422}{2}=211$.
## Step5: Solve for $y$
Substitute $x = 211$ into $y=x - 55$, we get $y=211-55 = 156$.
# Answer:
Number of sociology textbooks sold: 211
Number of psychology textbooks sold: 156