SOLUTION: Here is the word problem I am having complications solving: "Jeremy has 24 quarters and half dollars. If he had twice as many half dollars and half as many quarters, he would have

Question 395890: Here is the word problem I am having complications solving: "Jeremy has 24 quarters and half dollars. If he had twice as many half dollars and half as many quarters, he would have two dollars more. How much money does he have?" I did not know where to start with this problem. Please help me on this word problem. Thanks in advanced!
Answer by ankor@dixie-net.com(22740) (Show Source): You can put this solution on YOUR website!
Jeremy has 24 quarters and half dollars.
If he had twice as many half dollars and half as many quarters, he would have two dollars more.
How much money does he have?"
:
Let q = no. of quarters (originally)
let h = no. of half dollars
:
"Jeremy has 24 quarters and half dollars."
q + h = 24
h = (24-q)
:
"If he had twice as many half dollars and half as many quarters, he would have two dollars more."
The equation for this statement:
.50(2h) + .25(.5q) - [.50h + .25q] = 2.00
1h + .125q - .50h - .25q = 2
:
Combine like terms
1h - .5h + .125q - .250q = 2
.5h - .125q = 2
:
replace h with (24-q)
.5(24-q) - .125q = 2
12 - .5q - .125q = 2
-.625q = 2 - 12
-.625q = -10
q =
q = +16 quarters originally
then
h = 24 - 16
h = 8 half dollars originally
:
" How much money does he have?"
.50(8) + .25(16) =
4.00 + 4.00 = $8.00
:
:
Check solution in the statement:
"If he had twice as many half dollars and half as many quarters, he would have two dollars more."
.50(16) + .25(8) =
8 + 2 = $10
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