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 altogether 

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

### Step 1: Set up the relationships
We are given two key relationships:

1. Hillary has 24 fewer cards than Jerry:
   \[
   H = J - 24
   \]

2. 40% of Hillary's game cards is equal to 1/4 of Jerry's game cards:
   \[
   0.40H = \frac{1}{4}J
   \]

### Step 2: Solve the system of equations
We already know that \( H = J - 24 \), so substitute this into the second equation:

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

### Step 3: Solve for \( J \)
First, distribute the 0.40 on the left-hand side:

\[
0.40J - 9.6 = \frac{1}{4}J
\]

Now, to eliminate fractions, multiply the entire equation by 4:

\[
4(0.40J - 9.6) = J
\]

Simplify:

\[
1.6J - 38.4 = J
\]

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

\[
0.6J - 38.4 = 0
\]

Add 38.4 to both sides:

\[
0.6J = 38.4
\]

Finally, divide both sides by 0.6 to solve for \( J \):

\[
J = \frac{38.4}{0.6} = 64
\]

### Step 4: Find \( H \)
Since \( H = J - 24 \), we can substitute \( J = 64 \) into the equation:

\[
H = 64 - 24 = 40
\]

### Step 5: Find the total number of game cards
The total number of game cards is the sum of Hillary's and Jerry's cards:

\[
\text{Total} = H + J = 40 + 64 = 104
\]

Thus, Hillary and Jerry have 104 game cards altogether.

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Would you like further details on this solution? Here are 5 related questions to expand this problem:

1. How would the solution change if Hillary had 30 fewer cards than Jerry?
2. What if 50% of Hillary's cards equaled 1/3 of Jerry's cards?
3. Can you solve this problem by using a graph to represent the equations?
4. How many cards would each have if the difference between their cards doubled?
5. What is the effect on the total number of cards if both Hillary and Jerry gain 10 cards each?

**Tip:** When working with percentages, always convert them to decimals to simplify your calculations.

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 altogether?

Learn how to solve an algebraic word problem where Hillary has 24 fewer game cards than Jerry, and 40% of Hillary's cards is equal to 1/4 of Jerry's cards. This detailed solution walks through setting up equations and solving for the total number of game cards, ideal for students in Grades 7-9.

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