Solving a Fraction Word Problem

Rachel has 24 more markers than Sarah. If Sarah has 3/7 the number of markers Rachel has, how many markers do they have together? Let’s see how we can solve this… A Fraction Word Problem

Rachel has 24 more markers than Sarah. If Sarah has 3/7 the number of markers Rachel has, how many markers do they have together? First, let’s highlight or underline any information we think is important in the problem… R = # of markers Rachel has S = # of markers Sarah has Next, let’s define our variables. 1 2 3 Finally, let’s write equations to match the problem. R = 24 + S S = 3/7R

Rachel has 24 more markers than Sarah. If Sarah has 3/7 the number of markers Rachel has, how many markers do they have together? R = 24 + S S = 3/7 of R R = 24 + S S = 3/7R

Looking at our equations, we can see that the 24 markers more that Rachel has must be equal to 4/7 of her total markers. R = 24 + S Sarah’s Markers = 3/7R 24 = 4/7 Rachel’s markers = 24 + S = 24 + 3/7R If 4/7 of the markers represents 24, then 1/7 = 6 So 3/7 = 3x6=18. Therefore Sarah has 18 markers Rachel has 24 more than Sarah, so R = 18 + 24 = 42 markers Finally, Rachel’s markers + Sarah’s markers = 42 + 18 = 60 total markers S = 3/7R

So our final answer is 60 markers total. See if you can apply the same reasoning to the following problem: Our Answer Harry has 5/18 the number of Bertie Bott Beans Ron has. If Ron has 78 more beans than Harry, how many beans do they have altogether?