Question 169043
Try this:
Let a be the larger number and b the smaller number.
From the problem description, you have:
1) {{{a+b = 68}}} "The sum of the two numbers is 68." and ...
2) {{{a/b = 7}}}+{{{4/b}}} "If the larger number is divided by the smaller number, the quotient is 7 with a remainder of 4"
Rewrite equation 2) as:
{{{a = 7b+4}}} and substitute this into equation 1)
{{{(7b+4)+b = 68}}} Simplify.
{{{8b+4 = 68}}} Subtract 4 from both sides.
{{{8b = 64}}} Divide both sides by 8.
{{{b = 8}}} and
{{{a = 7b+4}}}
{{{a = 7(8)+4}}}
{{{a = 56+4}}}
{{{a = 60}}} The larger number is 60 and the smaller number is 8.
Check:
{{{a+b = 60+8}}}={{{68}}} Ok!
{{{a/b = 60/8}}}={{{7+4/8}}} or 7 + remainder of 4