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
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
and
Henry still has H.
We have two equations and two unknowns:
Cross-multiply them both
Solve by addition method.
Eliminate H by multiplying the first equation by -5 and the second equation
through by 2:
Add term by term:
Substitute in
Henry had 60.
Edwin
.
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
= .
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.