How to solve this ratio
The question doesn't give a ratio, so we'll just answer the question using symbols. A ratio is usually shown as two numbers separated by a colon like this A:B, where A and B are the two numbers. Let's take an example. The ratio of boys to girls in a class is A:B. This means that there are N(A+B) students in all, where N is a number. Let's say there are 22 students in the class, and the ratio of boys to girls is 5:6. Add 5 and 6=11, so A+B=11. 11N=22, so N=2. What fraction of the class are the boys? The number in the ratio for boys is 5, so 5/11 of the students are boys, that's 5/11 of 22=10. 6/11 of the class are girls, that's 6/11 of 22=12. 10+12=22, the number of students. So we can convert a ratio into fraction: A/(A+B) is the fraction of boys and B/(A+B) the fraction of girls. The number of boys is (A/(A+B))*N(A+B)=A*N; the number of girls is similarly B*N. The total number of students is A*N+B*N=N(A+B).
You can apply this conversion of ratios into fractions and actual numbers in all sorts of problems dealing with ratios. Here's another example. In a survey X people voted YES, Y people voted NO, and Z people couldn't decide, where X, Y and Z are given numbers. If P people were surveyed, what is the ratio of the people responding YES, NO and UNDECIDED? Here we have three classes of people so the ratio will look like x:y:z, where x, y and z are the numbers in the ratio. The total number of people is P=N(x+y+z). The fractions are x/(x+y+z), y/(x+y+z) and z(x+y+z). The numbers of people are Nx, Ny and Nz. But we know the actual numbers of people X, Y, and Z, so X=Nx, Y=Ny, Z=Nz, and, of course, X+Y+Z=P, the total number of people. But the fractions are also given by the actual numbers: X/P, Y/P, Z/P or X/(X+Y+Z), Y/(X+Y+Z), Z/(X+Y+Z), so the ratio could be expressed X:Y:Z. So we ignore N for the time being. Now let's work on an example. 750 people are surveyed. 375 voted YES, 300 voted NO and the rest were undecided. So X=375, Y=300. What is Z? Add X and Y: 675, so the rest is 750-675=75=Z. The ratio (first attempt) is X:Y:Z=375:300:75. Now, here's the trick. 75 goes into all these numbers so let's divide it: 5:4:1. That's the ratio in its neatest form, so x=5, y=4, z=1. (N=75.)
In some problems percentages may replace fractions, so in the case of the survey, 375/750 or 5/(5+4+1)=1/2 or 50%; 300/750 or 4/(5+4+1)=2/5 or 40%; 75/750 or 1/(5+4+1)=1/10 or 10%. Read More: ...