Let’s go through each problem one by one, solving them carefully.
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Problem 1:
Your brother traveled 117 miles in 2.25 hours. What’s the average speed?
Average speed = total distance ÷ total time
= 117 miles ÷ 2.25 hours
Let’s calculate:
2.25 × 50 = 112.5 → too low
2.25 × 52 = 2.25 × 50 + 2.25 × 2 = 112.5 + 4.5 = 117 → perfect!
So, 117 ÷ 2.25 = 52
✔ Average speed is
52 mph
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Problem 2:
You have 15 yards of ribbon for 20 gift boxes. Each box gets the same amount. How much per box?
Total ribbon ÷ number of boxes = 15 ÷ 20
That’s 15/20 = 3/4 yard per box.
✔ Each box gets
3/4 yard of ribbon.
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Problem 3:
Sam gave Jen 1/2 of his jujubes.
Jen ate 1/2 of what she got, then gave the rest to Kyle.
Kyle kept 8, gave 10 to Kim.
How many did Jen eat?
Let’s work backwards.
Kyle got some amount from Jen. He kept 8 and gave 10 to Kim → so Kyle received 8 + 10 = 18 jujubes.
Those 18 were “the rest” after Jen ate half → meaning Jen had twice that before eating: 18 × 2 = 36.
So Jen ate half of 36 → 18.
✔ Jen ate
18 jujubes.
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Problem 4:
Allowance savings:
Jan: $2
Feb: $4
Mar: $8
Apr: $16
... pattern doubles each month, through December (12 months).
This is a geometric sequence: 2, 4, 8, 16, ... up to 12 terms.
First term a = 2, ratio r = 2, n = 12.
Sum = a(rⁿ - 1)/(r - 1) = 2(2¹² - 1)/(2 - 1) = 2(4096 - 1) = 2 × 4095 = 8190
✔ Total saved:
$8,190
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Problem 5:
Staircase with 3 steps uses 6 cubes. How many for 11 steps?
Look at the diagram:
Step 1 (bottom): 3 cubes wide? Wait — actually, looking at the image description:
It says “6 cubes to build a staircase with 3 steps”.
Typically, a staircase like this means:
- Step 1 (top): 1 cube
- Step 2: 2 cubes
- Step 3: 3 cubes
Total = 1+2+3 = 6 → matches.
So for n steps, total cubes = 1 + 2 + 3 + ... + n = n(n+1)/2
For 11 steps: 11×12/2 = 66
✔ Need
66 cubes.
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Problem 6:
Jeff has 1/2 pizza left. At breakfast he ate 1/3 of it. What fraction of the ORIGINAL pizza is left for lunch?
He starts with 1/2 of original.
He eats 1/3 of that 1/2 → so he eats (1/3) × (1/2) = 1/6 of original.
Left after breakfast: 1/2 - 1/6 = 3/6 - 1/6 = 2/6 = 1/3
✔ He has
1/3 of the original pizza left for lunch.
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Final Answer:
1. 52 mph
2. 3/4 yard
3. 18
4. $8,190
5. 66
6. 1/3
Parent Tip: Review the logic above to help your child master the concept of 6th grade math word problems worksheet.
