# How Many Quarters Does She Have?

Juliet's purse contains 23 coins consisting of nickels and quarters, worth a total of \$3.35. How many quarters does she have?

11

12

10

13

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•  Juliet's purse contains 23 coins consisting of nickels and quarters,

worth a total of \$3.35.

many quarters does she have?

x + y = 23

5x + 25y = 335

20y = 220She has 11 quarters Answer: 11

• Michael's answer is correct as always.

But there is a different approach that lets you solve this problem using only trivial math.

Ever since you have been given a small number of answer choices, it is easy to solve this problem by logic instead of math.

In this case, a Guess Chart is a useful method.

QUARTERS | NICKELS | TOTAL VALUE

-----------------|---------------| -----------------------

10 . . . . . . . . | 13. . . . . . .|  250 + 65 = 315 ← First guess Wrong total

---------------------------------------------------------

11 . . . . . . . . | 12 . . . . . . | 275 + 60 = 335 ← Second guess ANSWER

Juliet has 11 quarters

• In order to solve for how many quarters there are, you need two formulas. And then have to use substitution to find your answer. Here is a handy and helpful graphic I put together to help you get your answer.

FYI, I also provided you with a double check to making sure your answer is correct. How? By solving for how many nickels. So you can first solve for the number of quarters. Or you can solve for the number of nickels first. If you do the math properly in both cases, your answers will match! Source(s): I've taught math plus many other subjects. And have helped out lots of students to help them better understand and learn.

10 Q & 17 N or

11 Q & 12 N or

12 Q & 7 N or

13 Q & 2 N

• q = number of quarters

n = number of nickels

23 coins consisting of nickels and quarters

q + n = 23

Subtract q from both sides

n = 23 - q

worth a total of \$3.35

multiply the number of coins by the value in cents

25q + 5(23 - q) = 335

Distribute

25q + 115 - 5q = 335

Subtract 115 from both sides

25q - 5q = 220

20q = 220

Divide both sides by 20

q = 11

11 quarters <––––––