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Difficulty: MediumBasic Ratios

A structural engineering team is mixing a specialized epoxy resin containing base, hardener, and silica filler in a strict ratio of 5:2:15:2:1 by weight. If the team uses exactly 3535 pounds of the base component, what is the total weight, in pounds, of the prepared epoxy mixture?

Answer: 56 pounds

Answer

The total weight of the prepared epoxy mixture is 56 pounds.
The components are mixed in a ratio of 5:2:15:2:1, which combines to make a total of 88 parts (5+2+1=85 + 2 + 1 = 8). We know the base component accounts for 55 of those parts and weighs 3535 pounds. This means a single part weighs 77 pounds (35÷5=735 \div 5 = 7). To find the total mixture weight, multiply the total number of parts (88) by the weight of a single part (77), resulting in 5656 pounds.

Step-by-Step Solution

1
Calculate the total number of parts in the given ratio.
5+2+1=85 + 2 + 1 = 8 total parts.
To establish the relationship between the individual components and the entire mixture.
2
Find the weight equivalent of one ratio part using the known base component.
35÷5=735 \div 5 = 7 pounds per part.
The base component represents 55 parts of the ratio and weighs 3535 pounds, so dividing its weight by its parts gives the unit multiplier.
3
Calculate the total weight of the mixture.
8×7=568 \times 7 = 56 pounds.
Multiplying the total number of ratio parts by the weight of a single part yields the overall total weight.

Key Concept

Solving part-to-whole ratio problems by finding the value of a single unit part.

Alternative Method

Calculate the individual weights of the missing components first. Hardener = 2×7=142 \times 7 = 14 pounds. Silica = 1×7=71 \times 7 = 7 pounds. Then, add these to the given base weight: 35+14+7=5635 + 14 + 7 = 56 pounds.
Estimated Time:1m 0s
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Topics

Basic Ratios

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