Christopher and Helen had 1044 erasers all together at first Christopher gave 4/5 of his erasers to his brother Helen gave 5/8 of her erasers to her sister in the end Helen had 150 erasers more than Christopher how many erasers did Christopher have at first

Let's define the number of erasers Christopher had initially as \( C \) and the number Helen had initially as \( H \). According to the problem, the total number of erasers is given by:

\[
C + H = 1044
\]

Christopher gave \(\frac{4}{5}\) of his erasers to his brother, so he has \(\frac{1}{5}\) of his erasers left:

\[
\text{Christopher's remaining erasers} = \frac{1}{5}C
\]

Helen gave \(\frac{5}{8}\) of her erasers to her sister, so she has \(\frac{3}{8}\) of her erasers left:

\[
\text{Helen's remaining erasers} = \frac{3}{8}H
\]

It is also given that in the end, Helen had 150 more erasers than Christopher:

\[
\frac{3}{8}H = \frac{1}{5}C + 150
\]

Now, we have a system of two equations:

\[
1) \ C + H = 1044
\]
\[
2) \ \frac{3}{8}H = \frac{1}{5}C + 150
\]

### Solving the system:

First, let's solve for \( C \) in terms of \( H \) from the first equation:

\[
C = 1044 - H
\]

Substitute this into the second equation:

\[
\frac{3}{8}H = \frac{1}{5}(1044 - H) + 150
\]

Now, multiply every term by 40 to eliminate the fractions:

\[
15H = 8(1044 - H) + 6000
\]

Distribute and simplify:

\[
15H = 8352 - 8H + 6000
\]

Combine like terms:

\[
15H + 8H = 14352
\]

\[
23H = 14352
\]

Solve for \( H \):

\[
H = \frac{14352}{23} = 624
\]

Now that we know \( H = 624 \), we can find \( C \):

\[
C = 1044 - 624 = 420
\]

### Final Answer:
Christopher had **420 erasers** at first.

Would you like a more detailed breakdown, or do you have any questions? Here are 5 related questions for further exploration:

1. How many erasers did Helen have initially?
2. How many erasers did Christopher give to his brother?
3. How many erasers did Helen give to her sister?
4. How many erasers did Christopher and Helen have in total after giving some away?
5. What fraction of their initial erasers do Christopher and Helen have remaining?

**Tip:** When dealing with word problems, translating the text into equations step by step helps keep track of all the information clearly.

Learn how to solve a word problem involving erasers where Christopher and Helen initially had 1044 erasers. Christopher gave away 4/5 of his erasers, and Helen gave away 5/8 of hers. Discover how many erasers Christopher had initially and how many erasers Helen had initially. Suitable for Grades 6-8.

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