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adelina 88 [10]
3 years ago
6

Vanessa earns a base salary of $400 every week with an additional 5% commission on everything she sells. Vanessa sold $1850 wort

h of items last week. What was Vanessa‘s total pay last week?
Mathematics
1 answer:
lys-0071 [83]3 years ago
6 0

Answer:

$492.50

Step-by-step explanation:

To start off, we already know that Vanessa makes at least $400 every week. What we don't know is how much Vanessa makes from her 5% commission on what she sells.

To solve for that, we need to find what 5% of $1,850 is. This can be done by multiplying $1,850 by 5%. Remember, we need to change 5% into its decimal form (5% -> \frac{5}{100} -> 0.05).

$1,850 x 0.05 = $92.5

This means that Vanessa made $92.5 off of commissions last week. The last step is to add her base salary of $400 to her commission sales and we get our final answer.

$400 + $92.5 = $492.50

Vanessa's total pay last week was $492.50

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Answer:

(x,y)=\left(\; \boxed{-1,-8} \; \right)\quad \textsf{(smaller $x$-value)}

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Step-by-step explanation:

Given system of equations:

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\begin{aligned}x^2-9&=4x-4\\x^2-4x-9&=-4\\x^2-4x-5&=0\end{aligned}

Factor the quadratic:

\begin{aligned}x^2-4x-5&=0\\x^2-5x+x-5&=0\\x(x-5)+1(x-5)&=0\\(x+1)(x-5)&=0\end{aligned}

Apply the <u>zero-product property</u> and solve for x:

\implies x+1=0 \implies x=-1

\implies x-5=0 \implies x=5

Substitute the found values of x into the <u>second equation</u> and solve for y:

\begin{aligned}x=-1 \implies y&=4(-1)-4\\y&=-4-4\\y&=-8\end{aligned}

\begin{aligned}x=5 \implies y&=4(5)-4\\y&=20-4\\y&=16\end{aligned}

Therefore, the solutions are:

(x,y)=\left(\; \boxed{-1,-8} \; \right)\quad \textsf{(smaller $x$-value)}

(x,y)=\left(\; \boxed{5,16} \; \right)\quad \textsf{(larger $x$-value)}

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