Maths tip: How many boys were there?

This is a tough question that helps with a bit of guessing (yes guess and check is a valid method).

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“In a school, the ratio of the number of pupils who wear glasses to the number of pupils who do not wear glasses is 11 : 5. 2/3 of the boys and 7/10 of the girls wear glasses. What is the ratio of the number of boys to the number of girls?”

Step 1: Write out the problem. It helps to divide the boys and girls into four categories – boys who wear glasses, boys who do not wear glasses, girls who wear glasses, and girls who do not wear glasses. You can lay it out in a table format as I have.

Step 2: Observe that the ratio of glasses to no glasses is 11:5. We need to adjust the ratios of boys and/or girls so that the numbers add up to give the ratio 11:5. In this case, it’s straightforward. Multiply the ratio of boys with glasses to boys without glasses by 2, and we get the solution.

Step 3: Boys to girls is 6 : 10 as shown in the table.