PROBLEM SET 4
Measurement Problems
1. Melissa's boyfriend gave her a 2 lb heart-shaped box of chocolates. The box had 68 pieces
of chocolate. What was the average weight for each piece of chocolate? (round to the nearest
hundredth)
Step 1. Understand the problem.
• What is asked?
- The average weight for each piece of chocolate in the 2 lb heart-shaped box
of chocolates given to Melissa
• How can I solve the problem?
- I must divide the weight of the heart-shaped box of chocolates into the 68
pieces of chocolate.
Step 2. Solve the problem.
• What are given?
Let x = the amount in grams for each piece of chocolate in the 2 lb heart-shaped box
of chocolates given to Melissa
Pounds can also be expressed in ounces.
•
1 lb = 16 oz; ∴ 2 lb = 32 0z
Solution:
𝑥=
32 𝑜𝑧
68
= 0.470588235 𝑜𝑧 ≈ 0.47 𝑜𝑧
Step 3. Check the answer
• Go back to the question asked.
• Have I answered the question asked?
- Based on how I represented x, yes.
• Have I rounded the answer to the nearest hundredth?
- Yes
Conclusion
Therefore, the average weight for each piece of chocolate in the 2 lb heart-shaped box
of chocolates given to Melissa is 0.47 oz.
.
2. The police went on a wild chase to catch a man speeding through town in a black pick-up
truck. At times their speeds exceeded eighty-five miles per hour. At that rate, how many miles
would the car go in 20 minutes? (round to the nearest whole mile)
Step 1. Understand the problem.
• What is asked?
- The number of miles that the car would go in 20 minutes considering their
speeds at 85 mph
• How can I solve the problem?
- Finding out how far can the car go in 20 minutes if they can reach 85 miles in
an hour
- Ratio and proportion can be used
Step 2. Solve the problem.
• What are given?
- Let x = the number of miles that the car would go in 20 minutes considering
their speeds at 85 mph
rate =
•
85 𝑚𝑖𝑙𝑒𝑠
1 ℎ𝑜𝑢𝑟
or
85 𝑚𝑖𝑙𝑒𝑠
60 𝑚𝑖𝑛𝑢𝑡𝑒𝑠
time = 20 minutes
x=?
Solution:
85 𝑚𝑖𝑙𝑒𝑠
60 𝑚𝑖𝑛𝑢𝑡𝑒𝑠
(85 𝑚𝑖𝑙𝑒𝑠)(20 𝑚𝑖𝑛𝑢𝑡𝑒𝑠)
60 𝑚𝑖𝑛𝑢𝑡𝑒𝑠
1700 𝑚𝑖𝑙𝑒𝑠∙𝑚𝑖𝑛𝑢𝑡𝑒𝑠
60 𝑚𝑖𝑛𝑢𝑡𝑒𝑠
=
𝑥
20 𝑚𝑖𝑛𝑢𝑡𝑒𝑠
=𝑥
=𝑥
28.33333333 𝑚𝑖𝑙𝑒𝑠 = 𝑥
28 𝑚𝑖𝑙𝑒𝑠 ≈ 𝑥
Step 3. Check the answer
• Go back to the question asked.
• Have I answered the question asked?
- Based on how I represented x, yes.
• Have I rounded the answer to the nearest whole mile?
- Yes
Conclusion
Therefore, the car would reach 28 miles in 20 minutes considering their speeds at 85
mph.
3. Kelsey has a new baby brother! He weighs 8 lbs 3 oz. The doctor said the baby should gain
about 5 ounces per week. At that rate, how much should the baby weigh in 3 months (12
weeks)? In lb and oz
Step 1. Understand the problem.
• What is asked?
- The weight of the baby in 12 weeks if he is currently 8 lbs 3 oz and would gain
5 oz per week
Step 2. Solve the problem.
• What are given?
Let x = the expected total weight of the baby in 12 weeks
Let y = the weight gained by the baby in 12 weeks
•
Present weight (z) = 8 lbs 3 oz
rate = 5 oz per week
time = 12 weeks
Solution:
In 12 weeks, the baby must gain:
5 oz (12) = 60 oz
or
1 𝑙𝑏
=
𝑦
16 𝑜𝑧
60 𝑜𝑧
(1 𝑙𝑏)(60 𝑜𝑧)
=𝑦
16 𝑜𝑧
60 𝑙𝑏𝑠 𝑜𝑧
=𝑦
16 𝑜𝑧
3.75 𝑙𝑏𝑠 = 𝑦
Converting 0.75 lb into ounces, we have:
0.75 (16 oz) = 12 oz
Hence:
y = 3 lbs 12 oz
x=z+y
x = 8 lbs 3 oz + 3 lbs 12 oz
x = 11 lbs 15 oz
Step 3. Check the answer
• Go back to the question asked.
• Have I answered the question asked?
- Based on how I represented x, yes.
• Have I expressed the answer in pounds and ounces?
- Yes
Conclusion
Therefore, the baby should weigh 11 lbs 15 oz in 12 weeks if he is currently 8 lbs 3
oz and would gain 5 oz per week .
4. Brad's father asked an engineer to survey the field behind their house. He wanted to plant
some orange and tangerine trees there. According to the survey, the field is thirty-two feet
long and six yards wide. What is the perimeter of the field in feet?
Step 1. Understand the problem.
• What is asked?
- The perimeter of the field in feet if it is 32-ft. long and six yards wide
• How can I solve the problem?
- By using this formula: P=2l+2w
Step 2. Solve the problem.
• What are given?
Let P = the perimeter of the field
l = 32 ft
1 yd. = 3ft.
w = 6 yards
w = 6 (3 ft) = 18 ft.
• Solution:
P = 2l + 2w
P = 2 (32 ft.) + 2 (18 ft.)
P = 64 ft. + 36 ft.\
P = 100 ft.
Step 3. Check the answer
• Go back to the question asked.
• Have I answered the question asked?
- Based on how I represented P and the formula I used, yes.
• Have I expressed the answer in feet?
- Yes
Conclusion
Therefore, the perimeter of the field is 100 ft.