Since I can’t see the image you uploaded, I’ll solve each of the four word problems based on the text you provided. These are classic ratio and proportion problems, often solved using tape diagrams (also called bar models), which visually represent parts of a whole.
Let’s go problem by problem.
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Problem 1:
> Riley and Justin shared a cash prize in the ratio 2:5. Justin received $27 more than Riley. How much money did Riley get?
Solution:
- Ratio = Riley : Justin = 2 : 5
- That means for every 2 parts Riley gets, Justin gets 5 parts.
- The difference in parts = 5 - 2 =
3 parts
- We’re told that this 3-part difference equals
$27
So:
→ 3 parts = $27
→ 1 part = $27 ÷ 3 =
$9
Riley got 2 parts → 2 × $9 =
$18
✔ Answer: Riley got $18
*(Tape diagram would show 2 boxes for Riley, 5 boxes for Justin — total 7 boxes. The extra 3 boxes between them equal $27.)*
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Problem 2:
> For every 3 drive-up Emily does, Clay does 2. If Emily did 30 drive-ups, how many more drive-ups did Emily do than Clay?
Solution:
- Ratio Emily : Clay = 3 : 2
- Emily did 30 drive-ups → This corresponds to 3 parts
→ So 3 parts = 30 → 1 part = 30 ÷ 3 =
10
Clay did 2 parts → 2 × 10 =
20 drive-ups
Difference = 30 - 20 =
10
✔ Answer: Emily did 10 more drive-ups than Clay
*(Tape diagram: 3 boxes for Emily = 30 → each box = 10; Clay has 2 boxes = 20)*
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Problem 3:
> Chloe, Katie, and Baker paid $18 for a gift for their mother. They shared the cost in the ratio 3:3:1. How much money did Chloe contribute?
Solution:
- Ratio = Chloe : Katie : Baker = 3 : 3 : 1
- Total parts = 3 + 3 + 1 =
7 parts
- Total cost = $18 → so 7 parts = $18
→ 1 part = $18 ÷ 7 ≈
$2.5714...
Chloe’s share = 3 parts → 3 × ($18/7) = $54/7 ≈
$7.71
But since money is usually expressed in cents, we can leave it as a fraction or decimal:
Exact value:
$54/7 or approximately
$7.71
✔ Answer: Chloe contributed $54/7 or about $7.71
*(Tape diagram: 3+3+1=7 boxes total. Each box = $18/7. Chloe has 3 boxes.)*
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Problem 4:
> Mr. Lopez has 24 more books than Mrs. Hill. If the ratio of their books is 7:4, how many books does Mrs. Hill have?
Solution:
- Ratio Lopez : Hill = 7 : 4
- Difference in parts = 7 - 4 =
3 parts
- This 3-part difference =
24 books
→ 3 parts = 24 → 1 part = 24 ÷ 3 =
8
Mrs. Hill has 4 parts → 4 × 8 =
32 books
✔ Answer: Mrs. Hill has 32 books
*(Tape diagram: Lopez = 7 boxes, Hill = 4 boxes. The 3 extra boxes = 24 books → each box = 8. Hill’s 4 boxes = 32.)*
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✔ Final Answers:
1.
Riley got $18
2.
Emily did 10 more drive-ups than Clay
3.
Chloe contributed $54/7 (≈ $7.71)
4.
Mrs. Hill has 32 books
Let me know if you’d like me to draw the tape diagrams for each problem!
Parent Tip: Review the logic above to help your child master the concept of ratio tape diagram worksheet.
