To solve this problem, we are going to set up a proportion. Let the variable x represent what we are trying to figure out, or the number of oil changes Frances can complete in 11 days. To set up this proportion, we are going to use our given values to make one ratio and then make a ratio that must be equivalent on the opposite side of the equation.
91 oil changes/7 days = x oil changes/11 days
To solve this proportion, we can cross-multiply. This means multiplying the numerator of one fraction by the denominator of the other fraction, and setting that equal to the product of the other numerator and denominator. This is modeled below:
91 * 11 = 7 * x
To simplify, we should do the multiplication on both sides of the equation.
1001 = 7x
Next, we have to divide both sides of the equation by 7 to get rid of the coefficient on the variable x and get it by itself.
x = 143
Therefore, Frances can complete 143 oil changes in 7 days.
Hope this helps!
