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
- Multiply by 85
- 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.
<h3>Answer:
x = (C-60)/85</h3>
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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.
<h3>Answers: 3 trips and 5 trips respectively</h3>
