Translating multistep word problems — Topic practice
5 exercises · 5 automatically checked · Untimed
Instructions and review guidance
5 questions · Shuffled order · Untimed practice
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Practice explanations
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The drill
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Question 1
Guide question E1.1
A delivery service charges $14 plus $3 per package. A 5% surcharge applies to the entire subtotal, and the final charge is $77.70. How many packages were delivered?
Enter an integer, decimal or fraction without units. Use up to 5 characters, or 6 including a leading minus.
Why this answer
20 packages
The surcharge multiplier applies to the entire subtotal, so 1.05(14 + 3n) = 77.70. Divide by 1.05 before subtracting the delivery fee: 14 + 3n = 74, then 3n = 60 and n = 20. Check the original bill: 1.05(14 + 60) = 77.70. Subtracting 14 directly from the total after the surcharge would mix a fee from before the surcharge with an amount after it. See Example 1.01.
An equal-weight data set has five values with mean 18. A sixth value is added, making the mean 20. What is the sixth value?
Enter an integer, decimal or fraction without units. Use up to 5 characters, or 6 including a leading minus.
Why this answer
30
The original five values total 5(18) = 90. The six values must total 6(20) = 120. The added value is therefore 120 − 90 = 30. Check: (90 + 30)/6 = 20. A mean is not an extra data value to be added to the list; it is a total divided by a count. See Example 1.03.
A runner covers 6 miles at 6 miles per hour and returns along the same route at 4 miles per hour. There are no stops. What is the average speed, in miles per hour, for the whole run?
Enter an integer, decimal or fraction without units. Use up to 5 characters, or 6 including a leading minus.
Why this answer
4.8 miles per hour
The total distance is 12 miles. The first 6 miles take 6/6 = 1 hour; the next 6 take 6/4 = 1.5 hours. Thus the average speed is 12/2.5 = 4.8 miles per hour. The average of 6 and 4 would be 5, but the two speeds were maintained for different amounts of time. See Example 1.06.
A 30-liter mixture is 40% juice by volume. Water is added, with no mixture removed and additive volumes, until the mixture is 25% juice. How many liters of water were added?
Enter an integer, decimal or fraction without units. Use up to 5 characters, or 6 including a leading minus.
Why this answer
18 liters
The amount of juice is fixed at 0.40(30) = 12 liters. If w liters of water are added, 12/(30 + w) = 0.25. Hence 30 + w = 48 and w = 18. The question asks for added water, not the 48-liter final volume. Check: 12/48 = 25%. See Example 1.07.
Two adjacent rectangular pens share a wall along one long side. There are three equal perpendicular fence segments and one long parallel fence. Exactly 60 meters of fencing is used. What is the maximum possible total area, in square meters?
Enter an integer, decimal or fraction without units. Use up to 5 characters, or 6 including a leading minus.
Why this answer
300 square meters
Two pens against a wall require one parallel length L and three perpendicular widths w, so L + 3w = 60. The area is A = wL = w(60 − 3w) = −3(w − 10)2 + 300. Its maximum is 300 at w = 10 and L = 30, which uses all 60 meters of fencing. Counting only two widths would omit the divider. See Example 1.15.