Exercise: Foundational Math
Questions for: Arithmetical Decimals
A small business tracks its daily operational costs. On Monday, expenses included $23.50 for office supplies and $45.75 for utilities. On Tuesday, the total expense for raw materials was double the combined expenses from Monday.
What was the total expenditure for both Monday and Tuesday?
A: $138.50
B: $207.75
C: $197.75
D: $204.75
Answer: B
1. Calculate Monday's total expenses: $23.50 (office supplies) + $45.75 (utilities) = $69.25.
2. Calculate Tuesday's total expenses: Tuesday's expenses were double Monday's total, so $69.25 * 2 = $138.50.
3. Calculate the total expenditure for both days: $69.25 (Monday) + $138.50 (Tuesday) = $207.75.
Why others are wrong:
A — This amount represents only Tuesday's total expenditure, not the combined total for both days.
B — Correct answer.
C — This result would occur if there was a calculation error when doubling Monday's expenses (e.g., $69.25 * 2 = $128.50 instead of $138.50), leading to $69.25 + $128.50 = $197.75.
D — This result would occur if there was a calculation error when summing Monday's initial expenses (e.g., $23.50 + $45.75 = $68.25 instead of $69.25), leading to a subsequent incorrect total for both days ($68.25 + ($68.25 * 2) = $68.25 + $136.50 = $204.75).
A baker begins with 2.75 kg of flour. He uses 1.2 kg for a cake and 0.35 kg for muffins. Realizing the cake needs more, he takes an additional 0.125 kg of flour from his stock to add to the cake mixture.
How much flour, in kilograms, does the baker have left after these operations?
A: 1.075 kg
B: 1.20 kg
C: 1.325 kg
D: 1.675 kg
Answer: A
1. Calculate the total amount of flour initially used: 1.2 kg (for cake) + 0.35 kg (for muffins) = 1.55 kg.
2. Subtract this amount from the initial flour stock: 2.75 kg - 1.55 kg = 1.2 kg.
3. The baker then uses an additional 0.125 kg of flour, which is also taken from his stock.
4. Subtract this additional amount from the current remaining stock: 1.2 kg - 0.125 kg = 1.075 kg.
5. Therefore, the baker has 1.075 kg of flour left.
Why others are wrong:
B — This would be the amount left if the additional 0.125 kg of flour was not taken from the stock.
C — This results from incorrectly adding the final 0.125 kg to the remaining stock instead of subtracting it.
D — This is the total amount of flour used in all operations, not the amount remaining.
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A baker needs to prepare a special cake. The recipe requires 0.75 kg of flour, 0.2 kg of sugar, and 0.05 kg of cocoa powder for the dry ingredients. After mixing these dry ingredients, the baker adds 0.35 kg of butter to the mixture.
What is the total weight of the ingredients after the butter has been added?
A: 1.25 kg
B: 1.35 kg
C: 1.45 kg
D: 1.55 kg
Answer: B
First, sum the weights of the dry ingredients:
0.75 kg (flour) + 0.20 kg (sugar) + 0.05 kg (cocoa powder) = 1.00 kg.
Next, add the weight of the butter to the sum of the dry ingredients:
1.00 kg (dry ingredients) + 0.35 kg (butter) = 1.35 kg.
The total weight of the ingredients is 1.35 kg.
Why others are wrong:
A — This result could occur if 0.25 kg of butter was mistakenly added instead of 0.35 kg.
B — Correct answer.
C — This result could occur if an extra 0.1 kg was incorrectly added, or if 0.05 kg was misread as 0.15 kg.
D — This result could occur from miscalculations, such as misreading 0.2 kg as 0.4 kg.
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A baker needs 12.5 kilograms of flour for a week. On Monday, he uses 3.75 kg for bread. On Tuesday, he uses an additional 4.2 kg for cakes.
How much flour does the baker have left for the rest of the week?
A: 4.55 kg
B: 7.95 kg
C: 8.75 kg
D: On Tuesday, he uses an additional 4.2 kg for cakes.
How much flour does the baker have left for the rest of the week?
A. 4.55 kg
B. 7.95 kg
C. 8.75 kg
D. 4.75 kg
Answer: A
First, calculate the total amount of flour used:
Flour used on Monday: 3.75 kg
Flour used on Tuesday: 4.20 kg (aligning decimal places for addition)
Total flour used = 3.75 + 4.20 = 7.95 kg
Next, subtract the total flour used from the initial amount of flour:
Initial flour: 12.50 kg (aligning decimal places for subtraction)
Total flour used: 7.95 kg
Flour remaining = 12.50 - 7.95 = 4.55 kg
Why others are wrong:
A — Correct calculation.
B — This is the total amount of flour used, not the amount remaining.
C — This result occurs if only the flour used on Monday (3.75 kg) is subtracted from the initial amount (12.5 - 3.75 = 8.75), ignoring the flour used on Tuesday.
D — This result occurs if there was an error in calculating the total flour used, for example, if 3.75 + 4.2 was incorrectly calculated as 7.75 (instead of 7.95), leading to 12.5 - 7.75 = 4.75.
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A shopper purchases groceries. They buy 2.5 kilograms of apples at a price of $3.20 per kilogram and 1.5 kilograms of bananas priced at $1.80 per kilogram.
If the shopper pays with a $20.00 bill, how much change should they receive?
A: $9.30
B: $10.70
C: $8.70
D: $10.30
Answer: A
Calculate the cost of apples: 2.5 kg * $3.20/kg = $8.00
Calculate the cost of bananas: 1.5 kg * $1.80/kg = $2.70
Calculate the total cost of groceries: $8.00 + $2.70 = $10.70
Calculate the change from a $20.00 bill: $20.00 - $10.70 = $9.30
Why others are wrong:
A — This is the correct amount of change.
B — This option represents the total cost of the groceries, not the change received.
C — This option results from an error in calculating the banana cost as $3.30 ($1.5 \times $1.80 is incorrectly calculated as $3.30 instead of $2.70), leading to a total of $11.30, and then $20.00 - $11.30 = $8.70.
D — This option results from a common subtraction error when calculating $20.00 - $10.70 (e.g., subtracting 0.7 from 0.0 directly without borrowing, leading to an incorrect difference of $10.30).
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