Question

Kelsey buys several pairs of uniform pants for $17.95 each and a sweater for 24Jeana shops at a different store and buys several pairs of uniform pants for $18.95 each plus a sweater for 18They set up the situation with the equation below, where x is the number of pairs of pantsIs there a situation in which they pay the same amount for their purchasesSelect all thermal correct represent the solution 17.95x+24=18.95x+18A. No solutions B. One solution C. Many solutions D. The girls will pay the same if they buy six pairs of pants and one sweater E. The girls will pay the same amount of any number of pants and one sweater Select all statements that correctly represent this situation in which they pay the same amount for their purchase

Answer 1

The given equation is

`17.95x+24=18.95x+18`

Let's solve for x. First, we subtract 17.95x from each side

`\begin{gathered} 17.95x-17.95x+24=18.95x-17.95x+18 \\ 24=x+18 \end{gathered}`

Then, we subtract 18 from each side

`\begin{gathered} 24-18=x+18-18 \\ x=6 \end{gathered}`

As you can observe, the equation has only one solution, which is x = 6. This means they will pay the same amount of money if they buy 6 pairs of pants, not any number but 6.

Hence, the right answers are B and D.