Ms. rao buys a computer, a printer, and a scanner for $2543. the computer cost $1502 more than the printer. the printer costs $123 more than that scanner. how much does ms. rao pay for computer?

This question involves a system of equations.

for the variables we will use c for computer, p for printer, and s for scanner.

in order to solve a system of equations, we need to solve one variable, so we will just pick c because we are solving for the computer.

when we set up the
equation, we need to convert all the variables into an applicable form of c, since that is the variable we are solving for. we can do this because we have information on how the other variables differ on c.

so we get these translations:

c = c
p = c - 1502
s = p - 123

however, the scanner is not translated to c yet, it is translated into p, but we know p can translate into c, so we plug in the equation for p as so:

s = (c - 1502) - 123

which translates to

s = c - 1625

now we have

c = c
p = c - 1502
s = c - 1625

now that we have the translations, we have to use the original equation given to us which is

c + p + s = 2543

which, with our translations can be said as

c + (c - 1502) + (c - 1625) = 2543

which simplifies to

3c - 3127 = 2543.

now, we add 3127 to both sides to get

3c = 5670

then, we divide 3 to both sides to get

c = 1890

so the computer costs 1890.

if you want to find the price for the printer and scanner, simply take c and plug it in to the other equations as so.

p = 1890 - 1502 (388)
s = 1890 - 1625 (265)