Theresa M. answered • 01/09/19
Pharmacology, Dosing Calculations, PTCB--- PharmD, ADHD-friendly Tutor
The beautiful thing about working with ratios is that everything moves in proportion to the other. It's kind of like how in an equation, whatever you do to one side you must do to the other, that same principle applies with ratios, too. In English, your ratio says that for every 8 boys, there are 7 girls. What if you multiplied it by two? For every 16 boys (8 times 2) you have 14 girls (7 times 2). See how I had to multiply 2 on both sides of the ratio?
In this problem, it might appear at first that you have two variables, two unknowns: the number of boys and the number of girls. But this is wrong, Because you were given the ratio, you really only have one single unknown, which is how many times bigger do you have to make this ratio to equal 135 total students? What if you multiplied it by three? If you have 24 boys (8 x 3) you have 21 girls (7 x 3). 24 plus 21 does not equal 135. We need to multiply this ratio by something bigger to get to 135 students.
Can you see the equation taking form? 8 times "some unknown number" plus 7 times "that same number" (because in a ratio, you do the same thing on both sides) equals 135. Can you solve it now?
