Question

Can someone please help me?

1.Modeling with mathematics: The total cost C (in dollars) to participate in a ski club is given by the literal equation C=85x+60, where x is the number of ski trips you take.

a. Solve the equation for x.

b. How many ski trips do you take if you spend a total of $315 and $485?​

Answer 1

Part (a)

We have some unknown number x which is a placeholder for a positive whole number (eg: x = 4).

What's happening to x are these two things, in this exact order

1. Multiply by 85
2. Add 60

We multiply first, then add. The order is important. We're following the order of operations PEMDAS here. If we knew what x was, then we'd go forward in the PEMDAS chain; however, we don't know what x is. So we go backwards in the chain to isolate x. This will undo every operation applied to x.

So,

C = 85x+60

C-60 = 85x

85x = C-60

x = (C-60)/85

In the second step, I subtracted 60 from both sides to undo the "plus 60" operation. Then in the last step, I divided both sides by 85 to undo the multiplication.

Answer:   x = (C-60)/85

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Part (b)

How many ski trips can we take if we spend $315? We simply plug in C = 315 into that equation we just found at the end of part (a).

Doing so gets us...

x = (C-60)/85

x = (315-60)/85

x = 255/85

x = 3

We can take 3 ski trips if we spent a total of $315

Repeat the same steps for C = 485

x = (C-60)/85

x = (485-60)/85

x = 425/85

x = 5

We can take 5 ski trips if we spent a total of $485

Note how plugging something like x = 5 into the original equation yields:

C = 85x+60

C = 85*5+60

C = 425+60

C = 485

Showing that x = 5 leads to C = 485. This helps confirm the second answer. I'll let you check the first answer.

Answers: 3 trips and 5 trips respectively