Rebecca S. answered • 01/29/20

Duke University science major; experience in mentorship and education

Hi Lydia!

In this problem, we are told that Jim and Krutika are sharing money in a 7:1 ratio. This is the same as saying that Jim gets 7/8 of the money, and Krutika gets 1/8. An easy way to transition between ratios and fractions is to add together the numbers in the ratio to get the denominator (bottom number) of the fraction. The numerator of the fraction (top number) will be the numbers given in the ratio.

Now that we know that 7/8 of the money is £66 more than 1/8 of the money, we can set up an equation, where x represents the total amount of money won:

(7/8) x = (1/8) x + 66

Let's subtract (1/8)x from both sides so we're working with fewer variables in the equation:

(7/8) x = (1/8) x + 66

-(1/8)x -(1/8)x

(6/8) x = 66

Now, let's divide both sides by (6/8) to get the value of x. Dividing by a fraction is the same as multiplying by its reciprocal, which in this case is 8/6:

(6/8) x = 66

×(8/6) ×(8/6)

x = 88

Now that we have the value of x, the total money won, we can use it to calculate Krutika's share. Remember that she is receiving 1/8 of the total money won. We can calculate this using x:

Krutika's share = (1/8)x = (1/8)(88) = 11

Krutika is getting £11.

I hope this helped, and feel free to ask any follow up questions or reach out to me for more help!

Rebecca S.