Math worksheet with age-related word problems to solve using one variable.

Since I can't view or access uploaded images directly, I can’t see the specific image you're referring to. However, based on your message, it appears that you've provided a list of word problems in text form (likely from an image), and you'd like me to solve them step by step.

Let’s go through each problem one by one, using only one variable when possible (as instructed), and explain the solution clearly.

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1. Mark is 4 years older than Jane. In 4 years, Mark will be 3/2 as old as Jane. How old is Jane now?

Let:
- $ J $ = Jane's current age
- Then Mark's current age = $ J + 4 $

In 4 years:
- Jane will be $ J + 4 $
- Mark will be $ (J + 4) + 4 = J + 8 $

Given: Mark will be $ \frac{3}{2} $ times as old as Jane:
$$
J + 8 = \frac{3}{2}(J + 4)
$$

Multiply both sides by 2:
$$
2(J + 8) = 3(J + 4)
\Rightarrow 2J + 16 = 3J + 12
\Rightarrow 16 - 12 = 3J - 2J
\Rightarrow J = 4
$$

✔ Jane is 4 years old now.

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2. Lucy is 4 times as old as Amy. Three years ago, Lucy was 13 times as old as Amy. How old is Lucy now?

Let:
- $ A $ = Amy’s current age
- Then Lucy’s current age = $ 4A $

Three years ago:
- Amy was $ A - 3 $
- Lucy was $ 4A - 3 $

Given:
$$
4A - 3 = 13(A - 3)
\Rightarrow 4A - 3 = 13A - 39
\Rightarrow -3 + 39 = 13A - 4A
\Rightarrow 36 = 9A
\Rightarrow A = 4
$$

So Lucy is $ 4A = 16 $

✔ Lucy is 16 years old now.

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3. In 15 years, Jenny will be three times as old as she is now. How old is she?

Let:
- $ J $ = Jenny’s current age

In 15 years: $ J + 15 $

Given:
$$
J + 15 = 3J
\Rightarrow 15 = 2J
\Rightarrow J = 7.5
$$

✔ Jenny is 7.5 years old (or 7 years and 6 months).

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4. 8 years ago, Jimmy was three times as old as Anne is now. Jimmy is 32. How old is Anne?

Jimmy is currently 32.

8 years ago, Jimmy was $ 32 - 8 = 24 $

That was three times Anne’s current age.

Let $ A $ = Anne’s current age

Then:
$$
24 = 3A \Rightarrow A = 8
$$

✔ Anne is 8 years old.

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5. Dustin is 11 years younger than Elias. In two years, Dustin will be half as old as Elias. How old is Dustin?

Let:
- $ D $ = Dustin’s current age
- Then Elias’s current age = $ D + 11 $

In two years:
- Dustin: $ D + 2 $
- Elias: $ D + 11 + 2 = D + 13 $

Given:
$$
D + 2 = \frac{1}{2}(D + 13)
$$

Multiply both sides by 2:
$$
2(D + 2) = D + 13
\Rightarrow 2D + 4 = D + 13
\Rightarrow D = 9
$$

✔ Dustin is 9 years old.

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6. Shawn is 40% as old now as he will be in 7 years. How old is he now?

Let:
- $ S $ = Shawn’s current age

In 7 years: $ S + 7 $

Given:
$$
S = 0.4(S + 7)
\Rightarrow S = 0.4S + 2.8
\Rightarrow S - 0.4S = 2.8
\Rightarrow 0.6S = 2.8
\Rightarrow S = \frac{2.8}{0.6} = \frac{28}{6} = \frac{14}{3} \approx 4.67
$$

✔ Shawn is $ \frac{14}{3} $ years old ≈ 4 years and 8 months.

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7. In 20 years, John will be 5 times as old as he is now. How old is he?

Let:
- $ J $ = John’s current age

In 20 years: $ J + 20 $

Given:
$$
J + 20 = 5J
\Rightarrow 20 = 4J
\Rightarrow J = 5
$$

✔ John is 5 years old.

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8. Kim is 3 times as old as Chase. How old is Kim?

This problem is incomplete — we don’t have enough information.

We need more data (e.g., sum of ages, difference, future/past condition).

✘ Not solvable with current info.

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9. Jeff is two years younger than Carrie. 12 years ago, Carrie was twice as old as Jeff. How old is Jeff?

Let:
- $ J $ = Jeff’s current age
- Then Carrie’s current age = $ J + 2 $

12 years ago:
- Jeff: $ J - 12 $
- Carrie: $ J + 2 - 12 = J - 10 $

Given:
$$
J - 10 = 2(J - 12)
\Rightarrow J - 10 = 2J - 24
\Rightarrow -10 + 24 = 2J - J
\Rightarrow 14 = J
$$

✔ Jeff is 14 years old.

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10. Steve is twice as old as Sylvie. Sylvie is three years older than Jacob. 4 years ago, Sylvie was twice as old as Jacob. How old is Sylvie?

Let:
- $ J $ = Jacob’s current age
- Then Sylvie = $ J + 3 $
- Steve = $ 2(J + 3) $

4 years ago:
- Jacob: $ J - 4 $
- Sylvie: $ J + 3 - 4 = J - 1 $

Given:
$$
J - 1 = 2(J - 4)
\Rightarrow J - 1 = 2J - 8
\Rightarrow -1 + 8 = 2J - J
\Rightarrow 7 = J
$$

So Sylvie is $ J + 3 = 10 $

✔ Sylvie is 10 years old.

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11. Jan is twice as old as Jake. The sum of their ages is 5 times Jake’s age less than 40. How old are Jan and Jake?

Let:
- $ J $ = Jake’s age
- Then Jan = $ 2J $

Sum of their ages: $ J + 2J = 3J $

“Sum of their ages is 5 times Jake’s age less than 40” → This phrase is ambiguous.

But likely means:
> Sum of their ages = 40 - 5 × Jake’s age

Or possibly:
> Sum = 5 × (Jake’s age) - 40?

But “less than 40” suggests:
$$
3J = 40 - 5J
\Rightarrow 3J + 5J = 40
\Rightarrow 8J = 40
\Rightarrow J = 5
$$

Then Jan = $ 2J = 10 $

Check: Sum = 5 + 10 = 15
Is 15 = 40 - 5×5 = 40 - 25 = 15 ✔

✔ Jake is 5, Jan is 10.

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✔ Final Answers:

| Problem | Answer |
|--------|--------|
| 1 | Jane is 4 years old |
| 2 | Lucy is 16 years old |
| 3 | Jenny is 7.5 years old |
| 4 | Anne is 8 years old |
| 5 | Dustin is 9 years old |
| 6 | Shawn is 14/3 ≈ 4.67 years old |
| 7 | John is 5 years old |
| 8 | Not enough information |
| 9 | Jeff is 14 years old |
| 10 | Sylvie is 10 years old |
| 11 | Jake is 5, Jan is 10 |

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Let me know if you'd like these explained further or formatted differently!