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Question 54025: In the following problem, (a) choose two variables to represent the numbers asked for, (b) write an open sentence relating the variables, and (c) solve the open sentence and give the answer to the problem. (Include solutions in which one of the variables is zero.)
Luis has 95 cents in dimes and quarters. Find all possibilities for the number of each type of coin he could have.
Answer by venugopalramana(3286)   (Show Source):
You can put this solution on YOUR website! In the following problem, (a) choose two variables to represent the numbers asked for, (b) write an open sentence relating the variables, and (c) solve the open sentence and give the answer to the problem. (Include solutions in which one of the variables is zero.)
Luis has 95 cents in dimes = D SAY and quarters = Q SAY. Find all possibilities for the number of each type of coin he could have.
TOTAL NUMBER OF DIMES AND QUARTERS = D+Q
VALUE OF DIMES = D*10=10D CENTS
VALUE OF QUARTERS =Q*25 = 25Q CENTS
TOTAL VALUE = 95 CENTS = 10D+25Q CENTS...
TO SOLVE WE SHOULD HAVE ANOTHER PARAMETER
LET THE TOTAL NUMBER OF COINS = 5
THEN D+Q = 5
D=5-Q
10(5-Q)+25Q=95
50-10Q+25Q=95
15Q=95-50=45
Q=3
D=2 IS ONE SOLUTION SET
IF YOU WANT ALL POSSIBILITIES THEN
Q=1....D=7
Q=3....D=2
THERE IS NO SOLUTION GOR D OR Q = 0 AS PER YOUR GIVEN DATA
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