Answer :

GinnyAnswer
To solve this problem, let's break it down step-by-step:

1. Define Variables:
- Let [tex]\(T\)[/tex] be the amount of money Tony has saved.
- Let [tex]\(S\)[/tex] be the amount of money Sarah has saved.

2. Analyze Given Information:
- The ratio of their savings is 7:11. This means for every £7 Tony has, Sarah has £11.
- Sarah has saved £24 more than Tony.

3. Express the Relationship Using the Ratio:
Since the ratio of Tony's savings to Sarah's savings is 7:11, we can write this as:
[tex]\[ \frac{T}{S} = \frac{7}{11} \][/tex]
This can be rearranged to:
[tex]\[ 11T = 7S \][/tex]

4. Utilize the Difference in Savings:
Given that Sarah has saved £24 more than Tony:
[tex]\[ S = T + 24 \][/tex]

5. Substitute and Solve:
Substitute [tex]\(S\)[/tex] from the relationship [tex]\(S = T + 24\)[/tex] into the equation [tex]\(11T = 7S\)[/tex]:
[tex]\[ 11T = 7(T + 24) \][/tex]
Now distribute and simplify:
[tex]\[ 11T = 7T + 168 \][/tex]
Combine like terms:
[tex]\[ 11T - 7T = 168 \][/tex]
[tex]\[ 4T = 168 \][/tex]
Solve for [tex]\(T\)[/tex]:
[tex]\[ T = \frac{168}{4} \][/tex]
[tex]\[ T = 42 \][/tex]

6. Find Sarah's Savings:
Substitute [tex]\(T\)[/tex] back into the equation [tex]\(S = T + 24\)[/tex]:
[tex]\[ S = 42 + 24 \][/tex]
[tex]\[ S = 66 \][/tex]

7. Calculate Total Savings:
Add Tony's savings and Sarah's savings to find the total savings:
[tex]\[ \text{Total savings} = T + S \][/tex]
[tex]\[ \text{Total savings} = 42 + 66 \][/tex]
[tex]\[ \text{Total savings} = 108 \][/tex]

So, the total amount Tony and Sarah have saved together is £108.

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