Graphing and Writing Linear Equations

Question

Question Number 1 The Math family paid a total of $21 to bowl 4 games and rent shoes. Each game cost $4. Write an equation to represent the total cost 𝒚 to rent shoes and bowl 𝒙 games. How much is shoe rental? How is this represented in the equation? 

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Question number 2. The amount Mo earns varies directly with the number of boxes of cookies she sells. How much does Mo earn for each box of cookies that she sells?

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Question Number 3 The Atlanta Zoo earns a profit of $8500 in January and $19,500 in June. What is the rate of change in profit for this time period? Hint - How many months occur in this problem?

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What information do we need to figure out?

Answer 1

Known: total cost (y) is $21

each game (x) is $4

the played 4 games (m)

need to find: cost for shoes (b)

Equation: y = mx+b

21 = 4(4)+b

21-16 = b

b= 5

The cost for shoes (b) is $5

Known: The closest intersection visible is when Mo earns $5 for selling 2 boxes.

Divide both numbers by 2 to find how much Mo earns for selling 1 box.

Mo earns $2.50 for each box of cookies he sells.

Known: January profit is $8500 ; June profit is $19500

Infer: Number of months from January to June is 5

Divide the difference in profit by the difference in months to find the rate of change.

19500-8500 = 1100

1100/5 =220

The rate of change of profit for this time period is $220 per month