Three times the larger of two numbers is equal to four times the smaller. The sum of the numbers is 21. How do you find the numbers?

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Answer 1 · 2017-01-07T22:26:04

See full process for solving this word problem below in the Explanation section:

Let us first deal with the first sentence of this word problem.

Let's call the larger number #l# and the smaller number #s#.

We know from the first sentence:

#3l = 4s#

We know from the second sentence:

#l + s = 21#

Let's solve this second equation for #s#:

#l - l + s = 21 - l#

#0 + s = 21 - l#

#s = 21 - l#

Now we can substitute #21 - l# for #s# in the first equation and solve for #l#:

#3l = 4(21 - l)#

#3l = 84 - 4l#

#3l + color(red)(4l) = 84 - 4l + color(red)(4l)#

#7l = 84 - 0#

#7l = 84#

#(7l)//color(red)(7) = 84/color(red)(7)#

#(color(red)(cancel(color(back)(7)))l)/cancel(color(red)(7)) = 12#

#l = 12#

Next we can substitute #12# for #l# in the solution to the second equation:

#s = 21 - 12#

#s = 9#

The larger number is 12 and the smaller number is 9