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Difficulty: HardDividing in a Ratio

A naval base allocates its quarterly maintenance budget among structural repairs, mechanical overhauls, and routine inspections in the ratio of 5:8:25:8:2. The amount allocated for mechanical overhauls is $45,000\$45,000 more than the amount allocated for routine inspections. Based on this information, calculate the total quarterly maintenance budget.

Answer:The total quarterly maintenance budget is $\$【112500】.

Answer

The total quarterly maintenance budget is $112,500.
The difference between the mechanical overhaul and routine inspection allocations represents 6 parts of the total ratio (8−28 - 2). By dividing the given dollar difference ($45,000\$45,000) by 6, we find that a single ratio part is worth $7,500\$7,500. Since the entire maintenance budget is composed of 15 parts in total (5+8+25 + 8 + 2), multiplying 15 by $7,500\$7,500 gives the correct total budget of $112,500\$112,500.

Step-by-Step Solution

1
Identify the number of ratio parts assigned to each category.
Structural = 55 parts, Mechanical = 88 parts, Routine = 22 parts.
This establishes the proportional distribution of the entire budget.
2
Determine the difference in parts between mechanical overhauls and routine inspections.
88 parts - 22 parts = 66 parts.
The problem provides the dollar amount for the difference between these two specific allocations, so we must find the corresponding difference in ratio parts.
3
Calculate the monetary value of a single ratio part.
$45,000÷6=$7,500\$45,000 \div 6 = \$7,500 per part.
Dividing the total monetary difference by the difference in parts gives the unit value of one part.
4
Find the total number of parts in the ratio and calculate the final budget.
Total parts = 5+8+2=155 + 8 + 2 = 15. Total budget = 15×$7,500=$112,50015 \times \$7,500 = \$112,500.
Multiplying the total number of parts by the value of a single part yields the overall budget.

Key Concept

Using the monetary difference between two shares in a ratio to determine the value of a single unit, which is then used to find the total amount.
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Topics

Dividing in a Ratio

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