Question

1. there are 35 boys in the seventh grade. the number of girls in the seventh grade is 42. lonnie says that means the ratio of the number of boys in the seventh grade to the number of girls in the seventh grade is 5:7. is lonnie correct? show why or why not.

Explanation:

Step1: Find the ratio of boys to girls

The number of boys is 35 and the number of girls is 42. So the ratio of boys to girls is $35:42$.

Step2: Simplify the ratio

To simplify the ratio $35:42$, we find the greatest common divisor (GCD) of 35 and 42. The factors of 35 are 1, 5, 7, 35 and the factors of 42 are 1, 2, 3, 6, 7, 14, 21, 42. The GCD of 35 and 42 is 7. We divide both parts of the ratio by 7: $\frac{35}{7}:\frac{42}{7}=5:6$.

Answer:

Lonnie is not correct. The ratio of the number of boys to the number of girls is $5:6$ (not $5:7$) because when we simplify the ratio $35:42$ by dividing both 35 and 42 by their GCD (7), we get $5:6$.