Question

What denominator for 21/3 = 49/? would make these ratios proportional?

Answer 1

[AI-generated answer — Bot GPT 3.5]

To determine the denominator that would make the ratios proportional, we need to find the missing value in the second ratio when the first ratio is 21/3 = 7.

We can set up a proportion:

21/3 = 49/x

To find x, we can cross multiply:

21 * x = 3 * 49

21x = 147

Dividing both sides by 21:

x = 7

Therefore, the denominator that would make the ratios proportional is 7, so 21/3 = 49/7.

Answer 2

wrong try again

Answer 3

[AI-generated answer — Bot GPT 3.5]

Apologies for the mistake.

To find the denominator that would make the ratios proportional, we can set up a proportion using the given ratios:
21/3 = 49/x

Cross multiplying, we have:
21x = 3 * 49

Dividing both sides by 3:
x = (3 * 49)/21

Reducing the fraction:
x = (3 * 7 * 7)/21

Canceling out common factors:
x = 1 * 7

Therefore, the denominator that would make the ratios proportional is 7. Hence, 21/3 = 49/7.

Answer 4

still wrong

Answer 5

[AI-generated answer — Bot GPT 3.5]

Apologies for the incorrect response.

To find the denominator that would make the ratios proportional, we can set up a proportion using the given ratios:
21/3 = 49/x

For two ratios to be proportional, the cross products must be equal. Cross multiplying, we have:
21x = 3 * 49

To solve for x, we need to divide both sides by 21:
x = (3 * 49) / 21

Simplifying the expression:
x = 7 * 7 / 3

In order to find the denominator that would make the ratios proportional, we need to choose a value for x that results in a whole number. The smallest value that works is when x = 7.

Therefore, the denominator that would make the ratios proportional is 7. The new ratio is 21/3 = 49/7.

Answer 6

[AI-generated answer — Explain Bot]

To find the denominator that would make the ratios proportional, we can use the concept of cross-multiplication.

Given: 21/3 = 49/?

To make these ratios proportional, we need to find a denominator for the second ratio that gives the same result when we cross-multiply.

To cross-multiply, we multiply the numerator of the first ratio by the denominator of the second ratio, and vice versa. In this case, it would be:

(21 * ?) = (3 * 49)

Now we need to find a number that makes the left side of the equation equal to the right side.

Let's solve for the missing value:

21 * ? = 3 * 49

Dividing both sides of the equation by 21:

? = (3 * 49) / 21

Simplifying:

? = 147 / 21

To reduce the fraction, we can divide the numerator and denominator by their greatest common divisor, which in this case is 21:

? = 7

So, to make the ratios 21/3 and 49/7 proportional, the denominator for the second ratio should be 7.