If pencils sell at 6 for 59 cents, how many pencils can be bought for $2.95?

1 Answer
Dec 21, 2016

So $2.95 will purchase 30 pencils

Explanation:

#color(red)("The shortcut method is much faster")#

1 cent purchases #6/59# of a pencil

so 295 cents purchases #" "color(green)(295xx6/59 = 30" pencils")#

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#color(blue)("Using first principle method of ratio")#

Note that $2.95 is the same value as 295 cents

Initial condition

#("pencil count")/("cost") ->6/59#

But we need #("pencil count")/("cost")=("pencil count")/295#

So we have:

#("pencil count")/("cost") ->6/59 -=("pencil count")/295#

So we need to change the 59 into 295. We do this by #xx295/59#

If we multiply the bottom by #xx295/59# we also need to multiply the top by the same number to maintain the correct proportions.

#("pencil count")/295 = (color(purple)(6xx295/59))/(59xx295/59)" "=" "30/295#

So $2.95 will purchase 30 pencils
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#color(blue)("Foot note")#

#color(purple)(6xx295/59) = (6xx295)/59 = color(green)(6/59xx295)" "# as in the shortcut method.