Question

Tree pruning company A charges a one-time $100 equipment fee and charges $50 for each tree that it prunes. Tree pruning company B charges a one-time $80 equipment fee and charges $60 for each tree that it prunes.

Let the variable t represent the number of trees pruned and let the variable c represent the cost.

For how many pruned trees will the cost be the same for both companies?

Which system of equations can be used to solve this problem?

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Responses

a {c=100−50tc=80−60t
a A system of equations. Row 1. c equals 100 minus 50 t. Row 2. c equals 80 minus 60 t

b {c=150tc=140t
b A system of equations. Row 1. c equals 150 t. Row 2. cquals 140 t.

c {c=50+100tc=60+80t
c A system of equations. Row 1. c equals 50 plus 100 t. Row 2. c equals 60 plus 80 t.

d {c=100+50tc=80+60t
d A system of equations. Row 1. c equals 100 plus 50 t. Row 2. c equals 80 plus 60 t.

Answer 1

Company A: c = 100 + 50t.
Company B: c = 80 + 60t.

So the correct system is option d: { c = 100 + 50t; c = 80 + 60t }.

Solve: 100 + 50t = 80 + 60t → 20 = 10t → t = 2.

The cost is the same when 2 trees are pruned (cost = $200).