SOLUTION: Roscoe and Conrad were counting money in their piggy banks. They only had quarters and dimes. They had a total of 58 coins. The value of the coins was $9.85. Find the number of
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-> SOLUTION: Roscoe and Conrad were counting money in their piggy banks. They only had quarters and dimes. They had a total of 58 coins. The value of the coins was $9.85. Find the number of
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Question 1157579: Roscoe and Conrad were counting money in their piggy banks. They only had quarters and dimes. They had a total of 58 coins. The value of the coins was $9.85. Find the number of quarters and dimes the boys had.
You can put this solution on YOUR website! Let = the number of dimes they had
Let = the number of quarters they had
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(1)
(2) ( in cents )
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(2)
Multiply both sides of (1) by
and subtract (1) from (2)
(2)
(1)
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and
(1)
(1)
(1)
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There are 31 dimes and 27 quarters
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check:
(2)
(2)
(2)
(2)
OK
Let d be the number of dimes.
Then the number of quarters is (58-d), according to the condition.
Then we can write the money equation for the total in the form
10d + 25*(58-d) = 985 cents.
From the equation, d = = 31.
ANSWER. 31 dimes and 58-31 = 27 quarters.
CHECK. 31*10 + 27*25 = 985 cents. ! Precisely correct !
An informal solution using logical reasoning and a bit of mental arithmetic....
(1) 58 coins all dimes would have a value of $5.80. The actual value is $9.85-$5.80 = $4.05 more.
(2) Exchanging a dime for a quarter keeps the number of coins at 58 and increases the total value by 15 cents.
(3) The number of dimes we need to exchange for quarters to make the additional $4.05 is 405/15 = 27.
