SOLUTION: The ratio of the number of muffins Elizabeth had to the number of muffins Henry had was 2:5. Elizabeth bought another 26 muffins. The ratio of the number of muffins Elizabeth had

Algebra ->  Percentage-and-ratio-word-problems -> SOLUTION: The ratio of the number of muffins Elizabeth had to the number of muffins Henry had was 2:5. Elizabeth bought another 26 muffins. The ratio of the number of muffins Elizabeth had      Log On


   

Question 1186669: The ratio of the number of muffins Elizabeth had to the number of muffins Henry
had was 2:5. Elizabeth bought another 26 muffins. The ratio of the number of
muffins Elizabeth had to the number of muffins Henry became 5:6. How many
muffins did Henry have?
Found 2 solutions by Edwin McCravy, ikleyn:
Answer by Edwin McCravy(20064) About Me  (Show Source):
You can put this solution on YOUR website!
I like taking each sentence separately and analyzing what it says before going
on to the next sentence.  Ikleyn likes to criticize my teaching methods. She
loves going straight to an equation without explaining why.

The ratio of the number of muffins Elizabeth had to the number of muffins Henry
had was 2:5.
 
Let's suppose:
Elizabeth had E muffins at first 
and 
Henry had H muffins.

So E%2FH=2%2F5

Elizabeth bought another 26 muffins.
 
So now Elizabeth has E+26 muffins

The ratio of the number of
muffins Elizabeth had to the number of muffins Henry became 5:6.
 
So %28E%2B26%29%2FH+=+5%2F6
and
Henry still has H.

We have two equations and two unknowns:

system%28E%2FH=2%2F5%2C%28E%2B26%29%2FH=5%2F6%29

Cross-multiply them both

system%285E=2H%2C6%28E%2B26%29=5H%29

system%285E=2H%2C6E%2B156=5H%29

system%285E-2H=0%2C6E-5H=-156%29

Solve by addition method. 
Eliminate H by multiplying the first equation by -5 and the second equation
through by 2:

system%28-25E%2B10H=0%2C12E-10H=-312%29

Add term by term:

-13E=-312
E=%28-312%29%2F%28-13%29
E=24

Substitute in

5E=2H
5%2824%29=2H
120=2H
120%2F2=H
60=H

Henry had 60.

Edwin

Answer by ikleyn(52882) About Me  (Show Source):
You can put this solution on YOUR website!
.
The ratio of the number of muffins Elizabeth had to the number of muffins Henry
had was 2:5. Elizabeth bought another 26 muffins. The ratio of the number of
muffins Elizabeth had to the number of muffins Henry became 5:6. How many
muffins did Henry have?
~~~~~~~~~~~ 

Based on the problem's description, you may think that E has 2x muffis; H has 5x muffins,

where x is the common factor, now unknown.


After E added 26 muffins, we have this equation 


    %282x+%2B+26%29%2F%285x%29 = 5%2F6.


To solve, cross multiply and simplify


    6(2x+26) = 5*(5x)

    12x + 6*26 = 25x

    6*26 = 25x - 12x

    6*26 = 13x

    6*2 = x

    x   = 12.


ANSWER.  Henry had 5x = 5*12 = 60 muffins.

Solved.

You may find that this way leads to the end in much more straightforward manner.