Sure, let's go through the problem step-by-step to understand how we arrive at the solution.
We are given the ratios of the stickers collected by Rosie, Matilda, and Ibrahim:
[tex]\[
\text{Rosie : Matilda : Ibrahim} = 4 : 7 : 15
\][/tex]
We also know:
1. Ibrahim has 24 more stickers than Matilda.
2. We need to find out how many more stickers Ibrahim has compared to Rosie.
To solve this, let's denote the number of stickers Matilda has by \( M \). Since the ratio between Matilda and Ibrahim is 7:15, we can express the number of stickers Ibrahim has in terms of Matilda's stickers:
[tex]\[
\text{Number of stickers Ibrahim has} = \frac{15}{7} \times M
\][/tex]
Given that Ibrahim has 24 more stickers than Matilda, we can set up the equation:
[tex]\[
\frac{15}{7} \times M = M + 24
\][/tex]
To solve for \( M \) (Matilda's stickers), let's first clear the fraction by multiplying through by 7:
[tex]\[
15M = 7M + 24 \times 7
\][/tex]
[tex]\[
15M = 7M + 168
\][/tex]
[tex]\[
15M - 7M = 168
\][/tex]
[tex]\[
8M = 168
\][/tex]
[tex]\[
M = \frac{168}{8}
\][/tex]
[tex]\[
M = 21
\][/tex]
So, Matilda has 21 stickers.
Using this, we can find out how many stickers Ibrahim has. Since Ibrahim has 24 more stickers than Matilda:
[tex]\[
\text{Ibrahim's stickers} = M + 24 = 21 + 24 = 45
\][/tex]
Next, to find out how many stickers Rosie has, we use the ratio 4:7. Given that Matilda has 21 stickers (which is the '7' part of the ratio):
[tex]\[
\text{Rosie's stickers} = \frac{4}{7} \times M = \frac{4}{7} \times 21 = 12
\][/tex]
Now, we need to find out how many more stickers Ibrahim has compared to Rosie:
[tex]\[
\text{Difference} = \text{Ibrahim's stickers} - \text{Rosie's stickers} = 45 - 12 = 33
\][/tex]
Therefore, Ibrahim has 33 more stickers than Rosie.
