in 17 - 19, use the sign at the right.\n17. write an algebraic expression that represents each purchase.\na…

in 17 - 19, use the sign at the right.\n17. write an algebraic expression that represents each purchase.\na. ms. martinez bought x number of litter boxes and 8 bags of cat food for the animal shelter.\nb. two sisters each bought 1 litter box, 10 cat toys, and x bags of cat food.\n18. communicate and justify suppose that x has the same value in both of the expressions you wrote in exercise 17. are the two expressions you wrote equivalent? explain.\n19. communicate and justify which costs the most: 12 cat toys, 4 bags of cat food, or 3 litter boxes? explain.

in 17 - 19, use the sign at the right.\n17. write an algebraic expression that represents each purchase.\na. ms. martinez bought x number of litter boxes and 8 bags of cat food for the animal shelter.\nb. two sisters each bought 1 litter box, 10 cat toys, and x bags of cat food.\n18. communicate and justify suppose that x has the same value in both of the expressions you wrote in exercise 17. are the two expressions you wrote equivalent? explain.\n19. communicate and justify which costs the most: 12 cat toys, 4 bags of cat food, or 3 litter boxes? explain.

Answer

Explanation:

Step1: Find the expression for part a

The cost of a litter box is $16$, so the cost of $x$ litter boxes is $16x$. The cost of a bag of cat food is $12$, so the cost of 8 bags of cat food is $12\times8 = 96$. The total cost is the sum of the cost of litter boxes and cat food. $$16x+96$$

Step2: Find the expression for part b

Each sister buys 1 litter box ($16$), 10 cat toys ($4\times10 = 40$), and $x$ bags of cat food ($12x$). Since there are 2 sisters, we multiply the sum of each sister's purchase by 2. $$2(16 + 40+12x)=2\times(56 + 12x)=112+24x$$

Answer:

a. $16x + 96$ b. $24x+112$