Question

(100 POINTS!)

Create a proportion using the form %/100= is/of to represent the following word problem:

15 is 1 1/2 % of what number?

Answer 1

To create a proportion using the form %/100 = is/of, we can first write the given information in the form %/100 = is/of. In this case, we know that 1 1/2% represents 15, so we can write:

1 1/2%/100 = 15/of

Next, we need to solve for the "of" value, which is the number we are trying to find. To do this, we can multiply both sides of the equation by 100 and then divide both sides by 1 1/2% to get:

(1 1/2%/100) * 100 = (15/of) * 100

of = (15/1 1/2%) * 100

Finally, we can evaluate the right-hand side of the equation to find the value of "of". Since 1 1/2% is the same as 1.5%, we can substitute 1.5 for 1 1/2% in the equation to get:

of = (15/1.5%) * 100

of = (15/0.015) * 100

of = 1000

Therefore, the number we are trying to find is 1000.

In summary, the proportion that represents the given word problem is:

1 1/2%/100 = 15/1000

Answer 2

`\textsf{Proportion}: \quad \sf (1.5)/(100)=(15)/(x)`

`\textsf{Solution}: \quad \sf x=1000`

Explanation:

Given proportion formula:

`\sf (\%)/(100)=(is)/(of)`

Given word problem:

• 15 is 1¹/₂% of what number.

Let the unknown number be x.

Therefore:

• % = 1.5
• is = 15
• of = x

Substitute these into the proportion formula to create a proportion to represent the given word problem:

`\sf (1.5)/(100)=(15)/(x)`

To solve the proportion, cross multiply:

`\implies \sf 1.5x=15 \cdot 100`

`\implies \sf 1.5x=1500`

Divide both sides by 1.5:

`\implies \sf (1.5x)/(1.5)=(1500)/(1.5)`

`\implies \sf x=1000`