A jar contains $36.25 in dimes and quarters. There are 250 coins in the jar. How many quarters are in the jar?

Question

Abigail Allen · Accepted Answer

There are 75 quarters in the jar.

First, write out both expressions from the word problem: #"A jar contains $36.25 in dimes and quarters"# we know that a quarter is worth $0.25 and a dime is worth $0.10, so let's rewrite this as an equation: #36.25=0.25q+0.1d# where #q# is the number of quarters and #d# is the number of dimes Now the second part of the problem: #"There are 250 coins in the jar"# This means that #q+d=250# To get the number of quarters as quickly as possible, we need to substitute the number of dimes from the second equation. we can do this by solving for #d# in the first equation: #362.5=2.5q+d rArr d=362.5-2.5q# now we can substitute that solution in the second equation: #q+(362.5-2.5q)=250# #-1.5q=-112.5# #color(red)(q=75)#

HIX Tutor · Answer

undefined Let's solve this step by step.

1. **Define Variables:**
   - Let $d$ be the number of dimes.
   - Let $q$ be the number of quarters.

2. **Set Up Equations:**
   - The total number of coins is 250:
     $$
     d + q = 250
     $$
   - The total value of the coins is $36.25, which is 3625 cents:
     $$
     10d + 25q = 3625
     $$

3. **Solve the First Equation for $d$:**
   - From $d + q = 250$:
     $$
     d = 250 - q
     $$

4. **Substitute into the Second Equation:**
   - Replace $d$ in the value equation:
     $$
     10(250 - q) + 25q = 3625
     $$
   - This simplifies to:
     $$
     2500 - 10q + 25q = 3625
     $$

5. **Combine Like Terms:**
   - Combine $ -10q + 25q $:
     $$
     2500 + 15q = 3625
     $$

6. **Isolate $q$:**
   - Subtract 2500 from both sides:
     $$
     15q = 1125
     $$
   - Now divide by 15:
     $$
     q = 75
     $$

7. **Final Answer:**
   - There are **75 quarters** in the jar.

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