And 3b = 4g, so b = 4g/3 = 4 × 12 / 3 = 16, so there are 16 boys So there are now 12 girls and 16 boys in the class, making 28 students altogether.
Check There are now 16 boys and 12 girls, so the ratio of boys to girls is 16 : 12 = 4 : 3 At the start of the year there were 20 boys and 10 girls, so the ratio was 20 : 10 = 2 : 1 Consecutive means one after the other.
And they are even, so they could be 2 and 4, or 4 and 6, etc.
We will call the smaller integer n, and so the larger integer must be n 2 And we are told the product (what we get after multiplying) is 168, so we know: n(n 2) = 168 We are being asked for the integers Solve: That is a Quadratic Equation, and there are many ways to solve it.
— and, trust me, you don't want to do this to yourself! Certain words indicate certain mathematica operations. But the order in addition doesn't matter, so it's okay to add backwards, because the result will be the same either way.) Also note that order is important in the "quotient/ratio of" and "difference between/of" constructions.
If a problems says "the ratio of Some times, you'll be expected to bring your "real world" knowledge to an exercise.
Using the Quadratic Equation Solver we get −14 and 12.
Check −14: −14(−14 2) = (−14)×(−12) = 168 YES Check 12: 12(12 2) = 12×14 = 168 YES So there are two solutions: -14 and -12 is one, 12 and 14 is the other.
Don't start trying to solve anything when you've only read half a sentence.
Try first to get a feel for the whole problem; try first to see what information you have, and then figure out what you still need. Figure out what you need but don't have, and name things. And make sure you know just exactly what the problem is actually asking for.