Answer:
Ann has $30
Ryan has $63
Keith has $21
Step-by-step explanation:
First I assigned variables to the amounts each owns. It doesn't really matter what letters, but I said x represents Ann's money, y represents Ryan's money, and z represents Keith's money.
We know that with all their money added up, they have 114. This gives us our first equation;
<u>114=x+y+z</u>
Ryan has 3 times what Keith has, which, in terms of variables, is
<u>y=3z</u>
Keith has nine dollars less than Ann. Less, in word problems, always means subtraction. This gives us our third equation:
<u> z=x-9</u>
Okay so the impulse is to put z=x-9 and y=3z into the first equation, but the goal is to create an equation with only one variable so this will not work.
What we do instead is sub z=x-9 into y=3z. This gives
<u>y=3(x-9)=3x-27</u>
Now that both y and z are in terms of x, we plug those equations into the first and then solve for x;
<u>114=x+3x-27+x-9</u>
<u>114=5x-36</u>
<u>150=5x</u>
<u>30=x</u>
Now that we know x, we can find z and y using the equations from earlier:
<u>z=30-9=21</u>
<u>y=3(21)=63</u>
x=30, y=63, and z=21, thus Ann has $30, Ryan has $63, and Keith has $21.