Question

Will, Sue and Micah went to dinner. Will paid 1/4 of the bill. Micah and Sue paid in the ratio of 1:3. If Sue paid $15 more than Will, how much did dinner cost in total?

Answer 1

The dinner costed $48 in total.

Explanation:

The amount of bill paid by Will = 1/4 of bill

Amount of bill paid by Micah and Sue 1: 3

Let us assume the common factor in the ratio = m

So, the amount paid by Micah = 1 x (m) = m

The amount paid by Sue = 3 x (m) = 3 m

Also, amount paid by Sue = $15 + Amount paid by Will

So, the amount paid by Will = amount paid by Sue - $15 = 3 m - $15

Total Bill = Bill amount paid by ( Will + Micah + Sue)

= m + 3 m + 3 m - 15 = 7 m - 15

Now, As will paid 1/4 of total bill.

⇒
`(1)/(4) * (7 m -15)  = 3m -15\\ \implies (7m - 15)  = 12  m - 60\\\implies 45 = 5 m \\\implies  m = 45/5 = 9`

or, m = 9

Now, the total bill = 7 m - 15 = 7(9) - 15 = $48

Hence, the dinner costed $48 in total.