Joseph's Books sold $741$ bookmarks this year. That is $90\%$ more than the store sold last year. How many bookmarks did Joseph's Books sell last year?

Full solution

Q. Joseph's Books sold

741

bookmarks this year. That is

90\%

more than the store sold last year. How many bookmarks did Joseph's Books sell last year?

Understand Problem: Understand the problem and identify what is given and what needs to be found. $\newline$ We are given that Joseph's Books sold $741$ bookmarks this year, which is $90\%$ more than last year. We need to find the number of bookmarks sold last year.
Let $x$ be Number: Let the number of bookmarks sold last year be $x$ . According to the problem, the number of bookmarks sold this year is $90\%$ more than last year. This means that this year's sales are $100\%$ of last year's sales plus an additional $90\%$ of last year's sales.
Translate into Equation: Translate the information into an equation. The equation to represent the situation is: $741 = x + 0.90x$
Combine Like Terms: Combine like terms to simplify the equation. $\newline$ $741 = 1x + 0.90x$ $\newline$ $741 = 1.90x$
Solve for x: Solve for x by dividing both sides of the equation by $1.90$ . $\newline$ $x = \frac{741}{1.90}$
Perform Division: Perform the division to find the value of $x$ . $x = 390$
Verify Solution: Verify that the solution makes sense in the context of the problem. If Joseph's Books sold $390$ bookmarks last year, then $90\%$ more would be $390 \times 0.90 = 351$ bookmarks more. Adding the additional bookmarks to last year's sales gives us $390 + 351 = 741$ bookmarks, which matches the number given for this year's sales.