Question

15 of 1815 of 18 Items
1




























































Skip to resources
Question
The picture is a scale drawing of a beanbag toss target that Morris made for his grandson’s birthday.






7.5 in.
6 in.
Scale
3 in. : 2 ft



Which equation can be used to determine x, the height of the beanbag toss target?
Responses
A
3 = x
2 7.5
3 = x 2 7.5
B 7.5x = 2(3)7.5 x = 2(3)
C
3 = 7.5
2 x
3 = 7.5 2 x
D 2x = 7.5(3)

Answer 1

To solve for the height of the beanbag toss target, we need to understand the scale relationship given in the problem: 3 inches in the drawing corresponds to 2 feet in reality.

Since we want to determine **x**, the height in the real-world measurements, we can set up a proportion based on the scale.

The relevant equation based on the scale factors can be derived as follows:

\[
\frac{3 \text{ in}}{2 \text{ ft}} = \frac{7.5 \text{ in}}{x \text{ ft}}
\]

Cross-multiplying gives:

\[
3 \cdot x = 2 \cdot 7.5
\]

This simplifies to:

\[
3x = 15
\]

So,

\[
x = \frac{15}{3} = 5 \text{ ft}
\]

Now, looking at the given options to see which one corresponds to our proportion:

- Option A: \( \frac{3}{2} = \frac{x}{7.5} \) (This could work)
- Option B: \( 7.5x = 2(3) \) (Rearranges to a solution but not in proportion)
- Option C: \( \frac{3}{2} = \frac{7.5}{x} \) (This represents the inverse, but we want to find x)
- Option D: \( 2x = 7.5(3) \) (This can also be rearranged effectively)

From these analyses, Option A appears to represent the correct proportion set up for determining x (since it aligns directly with the scale given).

### Therefore, the answer is:
**A: \( \frac{3}{2} = \frac{x}{7.5} \)**