How do you find the two numbers whose ratio is 3 to 4 and that have a sum of 35?

1 Answer
Alan P.
Jul 26, 2016

The two numbers are #{105/4, 35/4}#

Explanation:

Let the two numbers be #a# and #b# such that
[1]#color(white)("XXX")a/b=3#
and
[2]#color(white)("XXX")a+b=35#

From [1] (assuming this is a meaningful expression: #b!=0#)
we have
[3]#color(white)("XXX")a=3b#

Then substituting #3b# for #a# in [2]
[4]#color(white)("XXX")3b+b=35#
or
[5]#color(white)("XXX")b=35/4#

Combining [3] and [5]
[6]#color(white)("XXX")a=105/4#

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