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Elon is purchasing materials for a gardening project. Mulch costs 
$33 per cubic yard. Edge material costs 
$60 for 5 yards. Elon needs 60 yards worth of edge material. Let 
v be the volume, in cubic yards, of mulch that Elon buys; and let 
c be the total cost, in dollars, of his purchase. Which of the following equations correctly relates 
v and 
c ?
Choose 1 answer:
(A) 
33 v+720=c
(B) 
33 v+1,980=c
(c) 
33 v+3,600=c
(D) 
33 v+18,000=c

Elon is purchasing materials for a gardening project. Mulch costs $33 \$ 33 per cubic yard. Edge material costs $60 \$ 60 for 55 yards. Elon needs 6060 yards worth of edge material. Let v v be the volume, in cubic yards, of mulch that Elon buys; and let c c be the total cost, in dollars, of his purchase. Which of the following equations correctly relates v v and c c ?\newlineChoose 11 answer:\newline(A) 33v+720=c 33 v+720=c \newline(B) 33v+1,980=c 33 v+1,980=c \newline(C) 33v+3,600=c 33 v+3,600=c \newline(D) 33v+18,000=c 33 v+18,000=c

Full solution

Q. Elon is purchasing materials for a gardening project. Mulch costs $33 \$ 33 per cubic yard. Edge material costs $60 \$ 60 for 55 yards. Elon needs 6060 yards worth of edge material. Let v v be the volume, in cubic yards, of mulch that Elon buys; and let c c be the total cost, in dollars, of his purchase. Which of the following equations correctly relates v v and c c ?\newlineChoose 11 answer:\newline(A) 33v+720=c 33 v+720=c \newline(B) 33v+1,980=c 33 v+1,980=c \newline(C) 33v+3,600=c 33 v+3,600=c \newline(D) 33v+18,000=c 33 v+18,000=c
  1. Calculate total cost: Calculate the total cost of edge material.\newlineElon needs 6060 yards of edge material, and the cost of edge material is $60\$60 for 55 yards. To find the total cost for 6060 yards, we need to determine how many sets of 55 yards are in 6060 yards and then multiply by the cost per set.\newline60 yards5 yards per set=12 sets\frac{60 \text{ yards}}{5 \text{ yards per set}} = 12 \text{ sets}\newlineNow, multiply the number of sets by the cost per set:\newline12 sets×$60 per set=$72012 \text{ sets} \times \$60 \text{ per set} = \$720
  2. Write equation for cost: Write the equation relating the volume of mulch vv and the total cost cc. We know the cost of mulch is $33\$33 per cubic yard, so the cost for vv cubic yards of mulch is 33v33v dollars. We also know the total cost of edge material is $720\$720. Therefore, the total cost cc is the sum of the cost of mulch and the cost of edge material. So, the equation is: c=33v+$720c = 33v + \$720
  3. Match equation with choices: Match the equation from Step 22 with the given choices.\newlineThe equation we found is c=33v+($)720c = 33v + (\$)720, which matches choice (A)(A).

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