Question

Ernest and Gene have been saving coins every day for a sunny day in Arizona. Ernest has 8 more half dollars than Gene and no quarters. Gene has as many quarters as Ernest has half dollars, and each has 45 dimes. How many of each coin has each saved for the big day when $200 has been saved? Which of the following equations could represent the word problem if x is the number of half dollars that Gene has?a. 3x + 106 = 200

b. 125x + 916 = 20,000
c. 125x + 1,500 = 20,000

Answer 1

1. Ernest has $82.5 and Gene has $117.5

2. c) 125x + 1500 = $20000

Explanation:

If we mark Gene's half dollars with x, then it is given that Ernest has 8 more, which is x+8.

It is also given that Ernest has no quarters, but Gene has them as many as Ernest has half dollars, which is x+8.

And it is given that they both have 45 dimes each, which is $4.5 each.

Now, let's add up all these numbers:

Ernest: (x+8)•0.5 + 0•0.25 + 4.5 = 0.5x + 8.5

Gene: x•0.5 + (x+8)•0.25 + 4.5 = 0.75x + 6.5

They collected $200 together which means:

0.5x + 8.5 + 0.75x + 6.5 = $200

1.25x + 15 = $200

If we want to avoid decimal number, we can multiply whole equation with 100:

125x + 1500 = $20000

so, the correct answer is C.

Finally, to find x:

125x = 18500

x = 148

Ernest had 0.5x + 8.5 which is $82.5

Gene had 0.75x + 6.5 which is $117.5