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Question

Henry bakes 84 bread rolls and fruit muffins. After giving away 18 rolls, there are five sixth as many rolls as muffins left. How many rolls did henry bake?

Answer 1

Let's assume that Henry baked "x" rolls, then he baked (84 - x) muffins.

  5 
---- (x - 18) = 84 - x
  6 

Let's multiply both part of equation by 6

5(x - 18) = 6(84 - x)

5x - 90 = 504 - 6x

11x = 594

x = 54

Henry baked 54 rolls

Answer 2

Hi Bob;

R+M=84

Then he gave away...

R+M-18=84-18=66

R/M=5/6

We want only one variable...

(66-M)/M=5/6

Let's multiply both sides by M...

(M)[(66-m)/M]=(5/6)(M)

66-M=(5M)/6

Let's multiply both sides by 6...

6(66-M)=[(5M)/6](6)

6(66-M)=5M

396-6M=5M

Let's add 6M to both sides...

396-6M+6M=5M+6M

396=11M

36=Muffins

66-36=30 Rolls

 

Originally...

30 Rolls+18 Rolls=48 Rolls

(84 Rolls and Muffins)-(48 Rolls)=36 Muffins

 

Let's check our work...

Henry baked 48 Rolls and 36 Muffins, 84 Rolls and Muffins.  After giving away 18 Rolls, he now has 30 Rolls, 5/6th as many rolls as Muffins...

(30 Rolls)/(36 Muffins)

Let's divide both the numerator and denominator by 6...

[(30)/(6)]/[(36)/(6)]=5/6

Answer 3

r = # of rolls and m = # of muffins

84=r+m

take away 18 rolls and we have r-18 rolls

r-18=(5/6)m and r=18+(5/6)m

substitute into 84=r+m

                       84=18+(5/6)m+m

                       84-18=(1 5/6)m

                             66=(11/6)m

                       multiply both sides by 6/11

                              36=m

                         84-36=48

                              48=r

36 muffins and 48 rolls

check:48-18=30 rolls and (5/6) of 36=30 rolls