You are planning a 9 day trip to Texas. It will cost approximately $350 per day in Houston and $400 per day in San Antonio. If your budget for the trip is $3400, how many days can you spend in each place?

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Answer 1 · 2018-05-24T11:43:04

See a solution process below:

Let's call the number of days you will spend in Houston: #h#

And, let's call the number of days you will spend in San Antonio: #s#

We can then write these two equations:

#h + s = 9#

#$350h + $400s = $3400#

Step 1) Solve the first equation for #h#:

#h + s = 9#

#h + s - color(red)(s) = 9 - color(red)(s)#

#h + 0 = 9 - s#

#h = 9 - s#

Step 2) Substitute #(9 - s)# for #h# in the second equation and solve for #s#:

#$350h + $400s = $3400# becomes:

#$350(9 - s) + $400s = $3400#

#($350 * 9) - ($350 * s) + $400s = $3400#

#$3150 - $350s + $400s = $3400#

#$3150 + (-$350 + $400)s = $3400#

#$3150 + $50s = $3400#

#$3150 - color(red)($3150) + $50s = $3400 - color(red)($3150)#

#0 + $50s = $250#

#$50s = $250#

#($50s)/color(red)($50) = $250/color(red)($50)#

#(color(red)(cancel(color(black)($50)))s)/cancel(color(red)($50)) = 5#

#s = 5#

Step 3) Substitute #5# for #s# in the solution to the first equation at the end of Step 1 and calculate #h#:

#h = 9 - s# becomes:

#h = 9 - 5#

#h = 4#

With the budget and cost to stay in each city you can spend:
- 4 days in Houston
- 5 days in San Antonio