Diane took a math test. The ratio of the number of problems Diane got incorrect to the number of problems she got correct was 2:7. If the test had 36 questions on it, how many problems did she get correct?
is 2:7 the same ratio as 8:28 ? Magic. think how I did that.
To find out how many problems Diane got correct, we need to determine the number of problems she got incorrect first.
Let's assume the number of problems Diane got incorrect is 2x, and the number of problems she got correct is 7x.
According to the problem, the ratio of the number of problems she got incorrect to the number of problems she got correct is 2:7.
Therefore, 2x/7x = 2/7
We can now solve this equation to find the value of x.
Cross-multiplying, we have 2x * 7 = 2 * 7x
14x = 14x
Both sides have the same value, which means this equation is true for any value of x.
Thus, we can choose any value for x, such as x = 1.
When x = 1, the number of problems Diane got incorrect is 2(1) = 2, and the number of problems she got correct is 7(1) = 7.
Since the total number of problems on the test is 36, the number of problems she got correct is 7.