Jimmy set his score for his math test. After the math teacher returnee his paper to him, he realized that if he increased his ta
rget by 10%, he would need 1 more mark to reach his actual score. If he increased his target by 15%, this target would exceed his actual test marks by 3. What is his actual test score.
When ever you have percentages, it should be helpful to bear in mind you can express them as multipliers. In this case, it will be helpful. So, if we let: a = test score b = target score then, using the information given: a = 1.1b + 1 a = 1.15b - 3 and we get simultaneous equations. '1.1' and '1.15' are the multipliers that I got using the percentages. Multiplying a value by 1.1 is the equivalent of increasing the value by 10%. If you multiplied it by 0.1 (which is the same as dividing by 10), you would get just 10% of the value. Back to the simultaneous equations, we can just solve them now: There are a number of ways to do this but I will use my preferred method: Rearrange to express in terms of b: a = 1.1b + 1 then b = (a - 1)/1.1 a = 1.15b - 3 then b = (a + 3)/1.15 Since they are both equal to b, they are of the same value so we can set them equal to each other and solve for a: (a - 1)/1.1 = (a + 3)/1.15 1.15 * (a - 1) = 1.1 * (a + 3) 1.15a - 1.15 = 1.1a + 3.3 0.05a = 4.45 a = 89
