SOLUTION: this is the question: “How can I have $23.50 in change consisting of dimes, quarters, halves, and dollars with one third as many halves as dimes, twice as many quarters as dimes
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Question 1158500: this is the question: “How can I have $23.50 in change consisting of dimes, quarters, halves, and dollars with one third as many halves as dimes, twice as many quarters as dimes and 7 more dollars than halves”
Found 2 solutions by josgarithmetic, greenestamps:
Answer by josgarithmetic(39623) (Show Source): You can put this solution on YOUR website!
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$23.50 in change consisting of dimes, quarters, halves, and dollars with one third as many halves as dimes, twice as many quarters as dimes and 7 more dollars than halves
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d, q, h, D
dimes, quarters, half-dollars, DOLLARS
Substitute for D:
substitute for q:
Sub for d in that two-variable equation:
and from this find the numbers of the other coins.
Answer by greenestamps(13203) (Show Source): You can put this solution on YOUR website!
No! DON'T use 4 variables and write and solve a system of 4 equations...!
Take the time to analyze the given information and try to write a single equation.
The first piece of information is "one-third as many halves as dimes". We could let our variable x be the number of dimes; but then the number of halves would be (1/3)x. Fractions always make calculations more complicated; so let's start with our variable x as the number of halves. So
let x = # of half dollars
then 3x = # of dimes ["one third as many halves as dimes"]
then 6x = # of quarters ["twice as many quarters as dimes"]
then x+7 = # of dollars ["7 more dollars than halves"]
Now we have a single equation in one variable to solve -- far less work than solving a system of 4 equations and 4 unknowns.
Writing the equation in cents (again to avoid the difficulty of working with decimals):
ANSWER:
dollars: x+7 = 12
halves: x = 5
quarters: 6x = 30
dimes: 3x = 15
CHECK:
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