hillary has 24 fewer game cards then jerry. 40% of hillarys game cards is equal to 1/4 of jerrys game cards. how many game cards do they have altogether?

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

From the problem, we have 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: Express \( h \) in terms of \( j \)
From the first equation:
\[
h = j - 24
\]

### Step 2: Substitute \( h = j - 24 \) into the second equation
Substitute \( h = j - 24 \) into the second equation:
\[
0.4(j - 24) = \frac{1}{4}j
\]

### Step 3: Solve for \( j \)
First, distribute the 0.4 on the left-hand side:
\[
0.4j - 0.4 \times 24 = \frac{1}{4}j
\]
\[
0.4j - 9.6 = \frac{1}{4}j
\]

Next, convert \( \frac{1}{4}j \) to a decimal:
\[
0.4j - 9.6 = 0.25j
\]

Now, subtract \( 0.25j \) from both sides:
\[
0.4j - 0.25j = 9.6
\]
\[
0.15j = 9.6
\]

Finally, solve for \( j \) by dividing both sides by 0.15:
\[
j = \frac{9.6}{0.15}
\]
\[
j = 64
\]

### Step 4: Find \( h \)
Now that we know Jerry has 64 game cards, we can find how many Hillary has:
\[
h = j - 24 = 64 - 24 = 40
\]

### Step 5: Find the total number of game cards
The total number of game cards is the sum of Jerry's and Hillary's cards:
\[
j + h = 64 + 40 = 104
\]

Therefore, together they have **104 game cards**.

Would you like more details, or do you have any questions?

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Here are 5 related questions:
1. If Jerry had 10 fewer cards, how many cards would they have altogether?
2. What percentage of the total game cards does Hillary have?
3. If they decided to redistribute their cards evenly, how many cards would each person get?
4. If Hillary gave away 20% of her cards, how many cards would she have left?
5. What is the ratio of Jerry's cards to Hillary's cards after both lose 5 cards each?

**Tip:** When dealing with percentages, converting them to decimals often simplifies the calculations!

hillary has 24 fewer game cards than jerry. 40% of hillarys game cards is equal to 1/4 of jerrys game cards. how many game cards do they have altogether?

Learn how to solve a problem involving game cards, where Hillary has 24 fewer cards than Jerry, and 40% of her cards equals 1/4 of Jerry's cards. This step-by-step solution uses algebraic equations and is suitable for students in Grades 6-8.

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