Question 3346
To solve problems like this start by giving names to the integers. Call the bigger integer x and the smaller one y. Now, the problem tells us that the sum of x and y is 10. We can write this mathematically as:<br>
{{{x + y = 10}}}<br>
The problem also tells us that "three times the larger integer is three less then eight times the smaller integer." Let's break this up a little, three times the larger means three times x {{{3x}}} (x is the larger, right?). Next we are told that {{{3x}}} is three less than eight times the smaller. Well, eight times the smaller is {{{8y}}} and three less than {{{8y}}} is {{{8y - 3}}}. The problem says {{{3x}}} is {{{8y - 3}}} or, {{{3x = 8y - 3}}}.<br>
This gives us two equations:<br>
<ol>
<li>{{{x + y = 10}}} and</li>
<li>{{{3x = 8y - 3}}}</li>
</ol>

If we subtract y from both sides of the first equation, we get {{{x = 10 - y}}}<br>
Now substitute x in the second equation with {{{10 - y}}} and we get{{{3(10 - y) = 8y - 3}}}<br>
multiply 3 into the first part of the equation to get {{{30 - 3y = 8y - 3}}}<br>
add 3 to both sides to get {{{33 - 3y = 8y}}}<br>
add 3y to both sides to get {{{33 = 11y}}}<br>
finally, divide both sides by 11 to get {{{y = 3}}}.<br>
Since we know {{{x + 3 = 10}}}, we know {{{x = 7}}}