A company budgeted $73000 in total for project X and project Y, and the total actual spending is exactly as budgeted.
The actual spending on project X was 60% over its original budget, while project Y only used 80% of the planned budget.
Arrange the percentages of Project X and Y with budget and actual spending (in ‘000s)
The Correct Answer and Explanation is:
Let’s define the budgeted amounts for Project X and Project Y as follows:
- Let the budgeted amount for Project X be $x$ (in \$1,000s)
- Then the budgeted amount for Project Y is $73 – x$ (since the total budget is \$73,000 = 73 in \$1,000s)
Step 1: Use the information about actual spending
- Project X spent 60% over its budget, so actual spending = $x + 0.6x = 1.6x$
- Project Y spent only 80% of its budget, so actual spending = $0.8(73 – x)$
The total actual spending = \$73,000 = 73 (in \$1,000s), same as the total budget.
Step 2: Set up the equation
$$
1.6x + 0.8(73 – x) = 73
$$
Distribute the 0.8:
$$
1.6x + 58.4 – 0.8x = 73
$$
Combine like terms:
$$
0.8x + 58.4 = 73
$$
Subtract 58.4 from both sides:
$$
0.8x = 14.6
$$
Divide by 0.8:
$$
x = \frac{14.6}{0.8} = 18.25
$$
Step 3: Find budget and actual spending
- Project X:
- Budget: \$18,250 → 18.25 (‘000s)
- Actual: $1.6 \times 18.25 = 29.2$ → \$29,200
- Project Y:
- Budget: $73 – 18.25 = 54.75$ → \$54,750
- Actual: $0.8 \times 54.75 = 43.8$ → \$43,800
Final Answer (in ‘000s):
| Project | Budget (‘000s) | Actual Spending (‘000s) | % of Budget Used |
|---|---|---|---|
| X | 18.25 | 29.2 | 160% |
| Y | 54.75 | 43.8 | 80% |
🔍 Explanation (300+ words)
In this budget allocation problem, a company planned a total budget of \$73,000 for two projects—X and Y. However, the actual expenses for these projects varied: Project X went 60% over budget, while Project Y spent only 80% of its original budget. The key constraint is that the total actual spending remained the same as the original total budget, which was \$73,000.
To solve the problem, we assign a variable to the unknown budget of Project X—let’s call it $x$. Since the total budget is \$73,000, the budget for Project Y becomes $73 – x$. Using the percentage changes in actual spending, we calculate that Project X’s actual cost is 1.6 times its budget (due to the 60% overage), and Project Y’s actual cost is 0.8 times its budget (since it used only 80% of it).
We then set up an equation:
$$
1.6x + 0.8(73 – x) = 73
$$
This reflects the sum of the actual spending for both projects being equal to the total budget. Solving this equation yields $x = 18.25$, which means the budget for Project X was \$18,250, and therefore Project Y’s budget was \$54,750.
From here, we apply the actual spending percentages:
- Project X: $1.6 \times 18.25 = 29.2$ → \$29,200
- Project Y: $0.8 \times 54.75 = 43.8$ → \$43,800
Adding these two actual spending values gives the total of \$73,000, confirming the accuracy. Finally, we organize the values into a table showing each project’s budget, actual spending, and percentage of budget used. This clear breakdown ensures both numerical accuracy and conceptual understanding of budgeting variance.
