Question 904056
<pre>
["b=5n" is wrong because you can't set bananas equal to money.]


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you can buy b bananas for n nickels
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Therefore b bananas sell for 5n cents

Divide the bananas and the money both by b:

Therefore {{{b/b}}} or 1 banana sells for {{{5n/b}}} cents
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How many bananas can you buy for d dimes and q quarters?
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Suppose the answer is x bananas:

Since one banana sells for {{{5n/b}}} cents, 
x bananas sell for {{{5n*x/b}}} cents.

Now we see how much money is d dimes and q quarters:

d dimes is 10d cents and q quarters is 25q cents
So d dimes and q quarters is 10d+25q cents.
We can factor out 5, 5(2d+5q)

Set that equal to 5(2d+5q)

{{{5n*x/b}}}{{{""=""}}}{{{5(2d+5q)}}}

Multiply both sides by b to clear of fractions:

{{{5n*x}}}{{{""=""}}}{{{5b(2d+5q)}}}

Divide both sides by 5n

{{{x}}}{{{""=""}}}{{{(5b(2d+5q))/(5n)}}}

Cancel the 5's

{{{x}}}{{{""=""}}}{{{(b(2d+5q))/n}}}

That's the same as {{{(b/n)*(2d+5q)}}}, choice (a)

Edwin</pre>