Vance wants to have pictures framed. Each frame and mat costs $32 and he has at most $150 to spend. How do you write and solve an inequality to determine the number of pictures he can have framed?

Question

Hazel Anglin · Accepted Answer

Number of pictures can be framed is #4#

Let number of pictures can be framed is #x#

Cost of framing is #$32# for one picture.

#:. x*32 <=150 or x <= 150/32 or x <= 4.6875#

Number of pictures must be an integer.

#:. x =4 #

Hence number of pictures can be framed is #4# [Ans]

Genesis Allen · Answer

undefined Let $ x $ represent the number of pictures Vance wants to have framed. The total cost of framing $ x $ pictures is $ 32x $. Since Vance has at most $150 to spend, the inequality representing this situation is: 
$$ 32x \leq 150 $$
To solve for $ x $, divide both sides of the inequality by 32:
$$ x \leq \frac{150}{32} $$
$$ x \leq 4.6875 $$
Since Vance cannot have a fraction of a picture framed, the maximum number of pictures he can have framed is 4.