Question 825604
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Hi, there--

THE PROBLEM:
Delilah has a total of $1200 in a savings account and in a checking account. The ratio of 
money in savings to money in checking is 3 to 2. Use a system of equations to find how 
much money is in each account. 

A SOLUTION:

Define two variables.
Let c be the amount of money in Delilah's checking account (in dollars)
Let s be the amount of money in Delilah's savings account (in dollars)

Write two equations modeling the situation.

"Delilah has a total of $1200 in a savings account and in a checking account" translates to
{{{c + s = 1200}}}

"The ratio of money in savings to money in checking is 3 to 2."
{{{s/c=3/2}}}

Now solve the system of equations for c and s.

Rearrange the first equation to "c=" form.
{{{c=1200-s}}}

Substitute 1200-s for c in the second equation.
{{{s/(1200-s)=3/2}}}

Solve for s.
{{{2s=3(1200-s)}}}
{{{2s=3600-3s}}}
{{{5s=3600}}}
{{{s=720}}}

In the context of this problem, s=720 means Delilah has $720 in her savings account. This 
implies that she has $480 (1200-720=480) in her checking account.

We want to check that this ratio of money in savings to money is checking is indeed 3 to 2.
We scale down by a factor of 240. 

{{{720/240=3}}}
{{{480/240=2}}}

CHECK!

Hope this helps!
Mrs. Figgy
math.in.the.vortex@gmail.com
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