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Solved on Jan 18, 2024

Gina takes classes at two colleges. Westside fees are $98\$ 98 per credit, Pinewood fees are $115\$ 115 per credit. Gina takes 13 total credits. Express the total amount she paid.

STEP 1

Assumptions
1. Gina is taking a total of 13 credit hours at Westside Community College and Pinewood Community College combined.
2. The cost per credit hour at Westside Community College is 98.<br/>3.ThecostpercredithouratPinewoodCommunityCollegeis98.<br />3. The cost per credit hour at Pinewood Community College is 115.
4. Let ww represent the number of credit hours Gina is taking at Westside.

STEP 2

Calculate the total cost for the credit hours taken at Westside by multiplying the number of credit hours by the cost per credit hour at Westside.
Total cost at Westside=Cost per credit hour at Westside×Number of credit hours at WestsideTotal\, cost\, at\, Westside = Cost\, per\, credit\, hour\, at\, Westside \times Number\, of\, credit\, hours\, at\, Westside

STEP 3

Express the total cost for the credit hours taken at Westside in terms of ww.
Total cost at Westside=98wTotal\, cost\, at\, Westside = 98w

STEP 4

Since the total number of credit hours is 13, the number of credit hours taken at Pinewood is the remainder when we subtract ww from 13.
Number of credit hours at Pinewood=Total credit hours−Number of credit hours at WestsideNumber\, of\, credit\, hours\, at\, Pinewood = Total\, credit\, hours - Number\, of\, credit\, hours\, at\, Westside

STEP 5

Express the number of credit hours at Pinewood in terms of ww.
Number of credit hours at Pinewood=13−wNumber\, of\, credit\, hours\, at\, Pinewood = 13 - w

STEP 6

Calculate the total cost for the credit hours taken at Pinewood by multiplying the number of credit hours by the cost per credit hour at Pinewood.
Total cost at Pinewood=Cost per credit hour at Pinewood×Number of credit hours at PinewoodTotal\, cost\, at\, Pinewood = Cost\, per\, credit\, hour\, at\, Pinewood \times Number\, of\, credit\, hours\, at\, Pinewood

STEP 7

Express the total cost for the credit hours taken at Pinewood in terms of ww.
Total cost at Pinewood=115(13−w)Total\, cost\, at\, Pinewood = 115(13 - w)

STEP 8

Now, we need to find the combined total cost for all the credit hours taken at both Westside and Pinewood.
Combined total cost=Total cost at Westside+Total cost at PinewoodCombined\, total\, cost = Total\, cost\, at\, Westside + Total\, cost\, at\, Pinewood

STEP 9

Substitute the expressions found for the total costs at Westside and Pinewood into the combined total cost equation.
Combined total cost=98w+115(13−w)Combined\, total\, cost = 98w + 115(13 - w)

STEP 10

Now we can simplify the expression to find the combined total dollar amount Gina paid for her class fees.
Combined total cost=98w+115×13−115wCombined\, total\, cost = 98w + 115 \times 13 - 115w

STEP 11

Combine like terms by subtracting 115w115w from 98w98w.
Combined total cost=98w−115w+115×13Combined\, total\, cost = 98w - 115w + 115 \times 13

STEP 12

Simplify the expression by combining the ww terms.
Combined total cost=(98−115)w+115×13Combined\, total\, cost = (98 - 115)w + 115 \times 13

STEP 13

Calculate the numerical value of the coefficient of ww.
98−115=−1798 - 115 = -17

STEP 14

Multiply 115115 by 1313 to get the constant term.
115×13=1495115 \times 13 = 1495

STEP 15

Now, write the final expression for the combined total dollar amount Gina paid for her class fees.
Combined total cost=−17w+1495Combined\, total\, cost = -17w + 1495
The expression for the combined total dollar amount Gina paid for her class fees is −17w+1495-17w + 1495.

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