SOLUTION: The problem is a word problem that reads as follows:
Moira has $2.95 half dollars, dimes, and nickels. The number of half-dollars is 1 less than twice the number of dimes. The sum
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Moira has $2.95 half dollars, dimes, and nickels. The number of half-dollars is 1 less than twice the number of dimes. The sum
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Question 108375This question is from textbook Holt Algebra with Trigonometry
: The problem is a word problem that reads as follows:
Moira has $2.95 half dollars, dimes, and nickels. The number of half-dollars is 1 less than twice the number of dimes. The sum of the number of half-dollars and the number of nickels is 8. Find the number of coins of each type.
Please help me. I made three equations, and tried to solve the system but could not get the answer. It would be a big help. Thank you! This question is from textbook Holt Algebra with Trigonometry
You can put this solution on YOUR website! An equation for each if the 3 statements:
:
1.Moira has $2.95 half dollars, dimes, and nickels.
.05n + .10d + .5h = 2.95
:
2.The number of half-dollars is 1 less than twice the number of dimes.
h = 2d - 1
:
3.The sum of the number of half-dollars and the number of nickels is 8.
n + h = 8
:
Find the number of coins of each type.
Let's try to put n and d in terms of h
:
Rearrange equation 2:
2d - 1 = h
2d = h + 1
d =
or
d = .5(h+1)
d = (.5h+.5)
:
Rearrange equation 3:
n + h = 8
n = (8-h)
:
Back to eq 1: .05n + .10d + .5h = 2.95
:
Substitute (.5h+.5) for d & (8-h) for n; solve for h:
.05(8-h) + .10(.5h+.5) + .5h = 2.95
:
.4 - .05h + .05h + .05 + .5h = 2.95; group and combine like terms:
:
-.05h + .05h + .5h + .4 + .05 = 2.95
:
.5h + .45 = 2.95
:
.5h = 2.95 - .45
:
.6h = 2.50
:
h = 2.5/.5
:
h = 5 half dollars
:
Use n = 8 - h to find n
n = 8-5
n = 3 nickels
:
Use d = .5h + .5 to find d
d = .5(5) + .5
d = 2.5 + .5
d = 3 dimes
:
Check solution in the 1st equation:
.05(3) + .10(3) + .5(5) =
.15 + .30 + 2.5 = 2.95; confirms our solutions
:
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Did this help you? A lot of steps, but each one is logical, not hard to understand, is it?
