QuestionDefine a function $H(x)$ to calculate the cost after a 30% discount on Hector's original amount $x$ .

Studdy Solution

STEP 1

Assumptions1. The original cost that Hector needs to pay is represented by $x$ . The "good student discount" is30%
3. The discount is applied to the original cost

STEP 2

We need to find the amount of the discount. We can do this by multiplying the original cost by the discount rate.
$Discount = Original\, cost \\times Discount\, rate$

STEP 3

Now, we can define the function $H(x)$ as the original cost minus the discount.
$H(x) = Original\, cost - Discount$

STEP 4

Substituting the formula for the discount from2 into the function $H(x)$ , we get $H(x) = x - (x \\times Discount\, rate)$

STEP 5

Now, plug in the given value for the discount rate to define the function $H(x)$ .
$H(x) = x - (x \\times30\%)$

STEP 6

Convert the percentage to a decimal value.
$30\% =0.3$ $H(x) = x - (x \\times0.3)$

STEP 7

implify the function $H(x)$ .
$H(x) = x -0.3x$

STEP 8

Factor out $x$ from the function $H(x)$ .
$H(x) = x(1 -0.3)$

STEP 9

implify the function $H(x)$ .
$H(x) =.7x$ So, the function $H(x)$ that calculates the amount Hector needs to pay after a "good student discount" of $30 \%$ is applied is $H(x) =.7x$ .

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