I don't know how to make a formula for this word problem:
Two numbers are in the ratio of 7 to 10. If 24 is added
to each number, the resulting numbers are in the ratio
of 1 to 2. Find the smaller of the two original numbers.
Two numbers are in the ratio of 7 to 10
= 
which becomes upon cross-multiplying:
= 
If 24 is added to each number, the resulting numbers
are in the ratio of 1 to 2
= 
which becomes upon cross-multiplying:
= 
= 
= 
So we have this system of equations:
=
=
Solve that system of equations and the answer is
x = -42 and y = -60
The smaller is -60, because the SMALLER of two NEGATIVE
numbers is always the one with the LARGER absolute value.
So the answer is -60
Let's check: with the words:
-42 and -60 are in the ratio of 7 to 10 because the fraction
reduces to
If 24 is added to each number, we get -42+24 or -18, and
-60+24 or -36
-18 and -36 are in the ratio of 1 to 2 because the fraction
reduces to
Edwin
