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's denote the number of game cards Hillary has as \( H \), and the number of game cards Jerry has as \( J \).

### Step 1: Express the relationship between Hillary and Jerry's cards.
We are told:
- "Hillary has 24 fewer game cards than Jerry," so:
\[
H = J - 24
\]

### Step 2: Set up the equation for the second condition.
The second condition says that "40% of Hillary's game cards is equal to 1/4 of Jerry's game cards." We can express this as:
\[
0.4H = \frac{1}{4}J
\]

### Step 3: Substitute \( H = J - 24 \) into the second equation.
Substitute the value of \( H \) from the first equation into the second:
\[
0.4(J - 24) = \frac{1}{4}J
\]

### Step 4: Solve for \( J \).
First, distribute the 0.4 on the left-hand side:
\[
0.4J - 9.6 = \frac{1}{4}J
\]

Next, multiply through by 4 to eliminate the fraction:
\[
4(0.4J - 9.6) = J
\]
\[
1.6J - 38.4 = J
\]

Now, subtract \( J \) from both sides:
\[
1.6J - J = 38.4
\]
\[
0.6J = 38.4
\]

Finally, solve for \( J \):
\[
J = \frac{38.4}{0.6} = 64
\]

### Step 5: Find \( H \).
Now that we know \( J = 64 \), substitute this value back into the first equation to find \( H \):
\[
H = J - 24 = 64 - 24 = 40
\]

### Step 6: Find the total number of game cards.
The total number of game cards they have together is:
\[
H + J = 40 + 64 = 104
\]

Thus, Hillary and Jerry together have **104 game cards**.

Would you like more details or clarifications on any step?

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Here are 5 related questions to deepen your understanding:
1. If Hillary had 10 more cards, how would the total change?
2. What percentage of their combined cards does Jerry own?
3. If Jerry gave 5 cards to Hillary, how many cards would each have?
4. What if 30% of Hillary’s cards equaled 1/5 of Jerry’s cards?
5. How would the solution change if Hillary had 30 fewer cards instead of 24?

**Tip:** Always cross-check your final answers by substituting back into the original conditions to ensure correctness.

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?

This problem involves solving an algebraic equation where Hillary has 24 fewer game cards than Jerry. It explores the relationship between percentages and linear equations, ideal for students in Grades 6-8. Learn how to solve step-by-step.

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