Helen said to her sister Joanna, "I have five times as many stamps in my collection as you." "Yes, you have 240 more than I have," replied Joanna. How many stamps does Joanna have? Show your working for full marks.

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Let the number of stamps Joanna has be represented by $$ J $$.

According to Helen, she has five times as many stamps as Joanna, which can be expressed as:
$$
H = 5J
$$
where $$ H $$ is the number of stamps Helen has.

Joanna also states that Helen has 240 more stamps than she does:
$$
H = J + 240
$$

Now we have two equations:
1. $$ H = 5J $$
2. $$ H = J + 240 $$

Since both expressions equal $$ H $$, we can set them equal to each other:
$$
5J = J + 240
$$

Next, we will solve for $$ J $$. First, subtract $$ J $$ from both sides:
$$
5J - J = 240
$$
$$
4J = 240
$$

Now, divide both sides by 4:
$$
J = \frac{240}{4} = 60
$$

Thus, Joanna has $$ \boxed{60} $$ stamps.

To verify, we can calculate how many stamps Helen has:
$$
H = 5J = 5 \times 60 = 300
$$

Now, check the second condition:
$$
H = J + 240 \implies 300 = 60 + 240
$$
This is true, confirming that our solution is correct. Joanna has $$ \boxed{60} $$ stamps.Joanna has 60 stamps.

Helen said to her sister Joanna, “I have five times as many stamps in my collection as you.” “Yes, you have 240 more than I have,” replied Joanna.

How many stamps does Joanna have? Show your working for full marks.

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Helen said to her sister Joanna, “I have five times as many stamps in my collection as you.” “Yes, you have 240 more than I have,” replied Joanna. How many stamps does Joanna have? Show your working for full marks.