SOLUTION: Irving, the wishing well diver, has 10% as many quarters as nickels. if Irving has $5.25 in quarters and nickels, how many nickels does he have?

Question 1174345: Irving, the wishing well diver, has 10% as many quarters as nickels. if Irving has $5.25 in quarters and nickels, how many nickels does he have?
Found 3 solutions by math_tutor2020, josgarithmetic, ikleyn:
Answer by math_tutor2020(3817)   (Show Source): You can put this solution on YOUR website!

n = number of nickels
q = number of quarters
these values are some positive whole number

He has 10% as many quarters as nickels, meaning that,
q = 10% of n
q = (10/100)*n
q = 0.10n
This is equivalent to
10q = n
after multiplying both sides by 10
So n = 10q means that whatever number of quarters we have (q), we'll have ten times as many nickels (n).

For example, if we had 5 quarters, then
q = 5
n = 10q
n = 10*5
n = 50
Having 5 quarters leads to 50 nickels.

Irving has $5.25 in quarters and nickels. This is equivalent to 5.25*100 = 525 cents
Of that total value, 5n is from the nickels and 25q is from the quarters. So we have 5n+25q total cents which is set equal to 525

5n+25q = 525
5(n)+25q = 525
5(10q)+25q = 525 ... replace n with 10q, since n = 10q
50q+25q = 525
75q = 525
q = 525/75
q = 7
There are 7 quarters

If q = 7, then,
n = 10q
n = 10*7
n = 70
There are 70 nickels.

Let's check the answer
n = 70 nickels has a value of 5*n = 5*70 = 350 cents
q = 7 quarters has a value of 25*q = 25*7 = 175 cents
In total, we have 5n+25q = 350+175 = 525 cents = $5.25
This verifies the answer. Also note that 7 is 10% of 70 since 0.10*70 = 7.

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Answer: 70 nickels

Answer by josgarithmetic(39617)   (Show Source): You can put this solution on YOUR website!
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10% as many quarters as nickels.
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0.05*70+0.25*7=5.25
Answer by ikleyn(52786)   (Show Source): You can put this solution on YOUR website!
.

                    MENTAL solution

The condition says that the number of nickels is 10 times the number of quarters. So, you can group the coins in sets, placing 10 nickels and 1 quarter in each set. Then each set is worth 10*5 + 25 = 75 cents. Hence, the number of sets is = 7. It means, that Irving has 7 quarters and 7*10 = 70 nickels. ANSWER CHECK. 7*25 + 70*5 = 525 cents, in total. ! Correct !

Solved (mentally).

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On coin problems, see the lessons
    - Coin problems
    - More Coin problems
    - Solving coin problems without using equations
    - Kevin and Randy Muise have a jar containing coins
    - Typical coin problems from the archive
    - Three methods for solving standard (typical) coin word problems
    - More complicated coin problems
    - Advanced coin problems
    - Solving coin problems mentally by grouping without using equations
    - Non-typical coin problems
    - Santa Claus helps solving coin problem
    - OVERVIEW of lessons on coin word problems
in this site.

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The referred lessons are the part of this online textbook under the topic "Coin problems".

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