Question

Mrs. Smith decides to buy three sweaters and a pair of jeans. she had $120 in her wallet. if the price of jeans is $45,

what is the highest possible price (p) of a sweater, if each sweater, if each sweater is the same price? write, solve, and graph the inequality.

Answer 1

`3s+2j\leq $120`. The sweaters cost $10 or less each. We graph it on a number line at 10 and use a filled in dot pointing towards zero for less than.

Explanation:

Mrs. Smith buys 3 sweaters (represented by 3s) and 2 jeans (represented by 2j) for a total of at most $120. We don't know the total but we do know she couldn't spend more than $120.

We write
`3s+2j\leq $120`.

We know the jeans cost $45 each, so j=45. We substitute,

`3s+2(45)\leq $120\\3s+90\leq $120`

We solve for s by subtracting 90 to the other side and dividing the result by 3.

`3s+90-90\leq 120-90\\3s\leq 30\\(3s)/(3)\leq(30)/(3)`

`s\leq 10`.

The sweaters cost $10 or less each.