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.

Question

UpStudy AI · Accepted Answer

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.

Upstudy AI Solution

Answer

Solution

Extra Insights

Related Questions

Latest Algebra Questions

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.