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To build a deck, Roberto needs to buy 180 screws (s), 9 posts (p), and 36 pieces of 1" by 6" lumber (l). He already had the rest of the materials for the deck that he needs. An expression that represents his purchases is shown below:
180s + 9p + 36l

Part A:
Factor the expression that represents Roberto's purchases.

Part B:
The costs of buying the deck materials are shown in the chart below:
Material Cost
100 screw container $6.99
1 post $16.40
Set of 10 pieces of lumber $88.20
What materials does Roberto need to buy?

Part C:
What is the total cost to buy the deck materials (excluding tax)?

Respuesta :

The total cost of materials can be found from a list of materials based on the market unit rate.

The correct responses are;

  • Part A: The factored expression is; 9 × (20·s + p + 4·l)
  • Part B: The materials to be bought are; 2 cartons of screws, 9 pieces of posts, and 4 sets of 10 pieces of lumber.
  • Part C: The total cost of materials is $514.38.

Reasons:

Part A: The given expression representing the purchase is presented as follows;

Purchases = 180·s + 9·p + 36·l

Where;

s = Screws

P = Posts

l = Lumber

The factored expression is found as follows;

Purchases = 180·s + 9·p + 36·l = 9 × 20·s + 9·p + 9 × 4·l, which gives;

180·s + 9·p + 36·l = 9 × (20·s + p + 4·l)

The factored expression is; 9 × (20·s + p + 4·l)

Part B: The costs are;

100 screws  = $6.99

1 posts = $16.40

10 pieces of lumber = $88.20

The materials Roberto need to buy are;

180 screws, which can be obtained by buying 2 cartons of screws.

9 posts, which is obtained by buying 9 pieces of posts.

36 lumber which can be obtained by buying 4 × 10 pieces = 40 pieces of lumber.

Therefore, the, material Roberto needs to buy are;

2 cartons of screws

9 pieces of posts

40 pieces of lumber

Part C: The total cost of the materials are therefore;

2 cartons of screws × $6.99 per carton = $13.98

9 pieces of posts × $16.40 per piece = $147.6

4 Sets of 10 pieces of lumber × $88.20 per set = $352.8

The total cost = $13.98 + $147.6 + $352.8 = $514.38

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