Hillary has 24 fewer game cards than Jerry.40% of Hillary’s game cards is equal to 1/4 of Jerry game cards. How many game cards do they have together 

Let the number of game cards Jerry has be denoted by \( J \), and the number of game cards Hillary has be denoted by \( H \).

We are given two pieces of information:

1. Hillary has 24 fewer game cards than Jerry:
   \[
   H = J - 24
   \]
   
2. 40% of Hillary’s game cards is equal to 1/4 of Jerry's game cards:
   \[
   0.4H = \frac{1}{4}J
   \]

### Step 1: Substituting \( H \) from the first equation into the second equation
Substitute \( H = J - 24 \) into the equation \( 0.4H = \frac{1}{4}J \):

\[
0.4(J - 24) = \frac{1}{4}J
\]

### Step 2: Solve for \( J \)
Distribute the 0.4 on the left-hand side:

\[
0.4J - 9.6 = \frac{1}{4}J
\]

Multiply the entire equation by 10 to eliminate the decimals:

\[
4J - 96 = 2.5J
\]

Now, subtract \( 2.5J \) from both sides:

\[
4J - 2.5J = 96
\]

This simplifies to:

\[
1.5J = 96
\]

Divide both sides by 1.5:

\[
J = \frac{96}{1.5} = 64
\]

So, Jerry has 64 game cards.

### Step 3: Find the number of game cards Hillary has
Now that we know Jerry has 64 game cards, we can use the equation \( H = J - 24 \) to find Hillary's game cards:

\[
H = 64 - 24 = 40
\]

### Step 4: Find the total number of game cards they have together
The total number of game cards is:

\[
J + H = 64 + 40 = 104
\]

### Final Answer: 
Together, Hillary and Jerry have 104 game cards.

Would you like a detailed breakdown of any step?

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Here are 5 related questions to expand your understanding:

1. How do you solve similar percentage-based algebra problems?
2. Can you explain how to solve systems of equations by substitution?
3. How would this problem change if Jerry had 24 fewer cards than Hillary?
4. What happens if we change 40% to another percentage, say 50%?
5. Can we solve the same problem using graphing techniques?

**Tip**: Always write out relationships clearly in word problems, then convert them into mathematical equations for easy solving.

Hillary has 24 fewer game cards than Jerry. 40% of Hillary’s game cards is equal to 1/4 of Jerry's game cards. How many game cards do they have together?

Learn how to solve a word problem where Hillary has 24 fewer game cards than Jerry, and 40% of Hillary's cards equals 1/4 of Jerry's cards. This solution covers key algebraic concepts such as substitution and solving linear equations, suitable for students in Grades 6-8.

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