Janelle and her best friend Carmen go shopping. The function p(x) = 5x4 − 3x3 + 2x2 + 24 represents how much money each girl spent based on the number of hours they were shopping. If Janelle and Carmen each go shopping for 2 hours, how much money did they spend together?

$58
$62
$176
$124

1 answer

To determine the total amount of money that Janelle and Carmen spent together after 2 hours of shopping, we need to evaluate the function \( p(x) \) at \( x = 2 \).

The function given is:

\[ p(x) = 5x^4 - 3x^3 + 2x^2 + 24 \]

To find \( p(2) \), we substitute \( x = 2 \) into the function:

\[ p(2) = 5(2)^4 - 3(2)^3 + 2(2)^2 + 24 \]

Now, we calculate each term step by step:

\[ 5(2)^4 = 5 \times 16 = 80 \]
\[ -3(2)^3 = -3 \times 8 = -24 \]
\[ 2(2)^2 = 2 \times 4 = 8 \]

Summing these results along with the constant term:

\[ 80 - 24 + 8 + 24 = 88 \]

So, \( p(2) = 88 \).

Since both Janelle and Carmen spent the same amount of money and both were shopping for 2 hours, we need to calculate their combined expenditure:

\[ 88 + 88 = 176 \]

Therefore, the total amount of money spent by Janelle and Carmen together is:

\[ \boxed{176} \]