Question

At the not much fun amusement park, Otaka Shawa paid $25.75 for three game of mini-marbles-golf and two rides on the slow-go-karts,while Soren Derkeister paid $35.75 for four games of mini-marbles-golf and three rides on the slow-go-karts. How much did each activity cost?

Answer 1

I’ll use m for marbles & g for go karts. I’m hoping someone has a prettier way to do this, and I can learn with you.

3m + 2g = 25.75
4m + 3g = 35.75

We’ll take the top equation and solve for g in terms of m.

2g = -3m + 25.75
g = (-3m + 25.75)/2

Then substitute that mess, um, expression, I to the second equation to solve for m.

4m + 3[(-3m + 25.75)/2] = 35.75
4m + (-9m + 77.25)/2 = 35.75
4m -4.5m + 38.625 = 35.75
-0.5m = -2.875
0.5m = 2.875
m = 5.75

Now we pick an equation, plug in the numerical value of m, and solve for a numerical value of g

3m + 2g = 25.75
3(5.75) + 2g = 25.75
17.25 + 2g = 25.75
2g = 8.50
g = 4.25

Checking the math:
4m + 3g = 35.75
4(5.75) + 3(4.25) = 23 + 12.75 = 35.75

Mini marbles golf cost $4.25, slow go karts cost $5.75.