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1 month ago

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Zoe paid \$18.60$18.60dollar sign, 18, point, 60 in sales tax and tips for her dinner. The sales tax rate is 11\%11%11, percent,

and she tipped 20\%20%20, percent. (The sales tax does not apply to the tip, and the tip is based on the price of the dinner before sales tax.) What was the price of Zoe's dinner, before sales tax and tip?

2 answers:

Svet_ta [12.7K]1 month ago

6 0

Zoe incurred $18.60 in tips and sales tax for her meal. The rate of sales tax stands at 11% while her tip amounted to 20%. (The tip does not include sales tax, and it is calculated on the dinner's price before tax.)

From the information provided, it's evident that both the tip and sales tax apply solely on the dinner cost. Thus, we have:-

Sales Tax = 11% of dinner cost

Tip = 20% of dinner cost

And Sales Tax + Tip = $18.60

Therefore, (20+11)% of dinner cost = 18.60

31% of dinner cost = 18.60

0.31 * dinner cost = 18.60

dinner cost = 18.60/0.31 = 60

Thus, Zoe's dinner cost was $60.

Svet_ta [12.7K]1 month ago

6 0

Conclusion:

$60

Detailed explanation:

sourced from khan

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Detailed breakdown:

The functions involved are

$f(x)=-x^{2}+4x+12$

$g(x)=-x+6$

Step 1:

Insert $x=1$ in $f(x)=-x^{2} +4x+12$ to find the value of $f(1)$ .

$f(1)=-1^{2} +4(1)+12\\f(1)=-1+4+12\\f(1)=15$

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Step 2:

Insert $x=2$ in $f(x)=-x^{2} +4x+12$ to obtain the value of $f(2)$ .

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Substitute $x=2$ into $g(x)=-x+6$ to find the value of $g(2)$ .

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Step 3:

Replace $x=3$ in $f(x)=-x^{2} +4x+12$ to find the value of $f(3)$ .

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Also, replace $x=3$ in $g(x)=-x+6$ to find the value of $g(3)$ .

$g(3)=-3+6\\g(3)=3$

Step 4:

Insert $x=4$ in $f(x)=-x^{2} +4x+12$ to find the value of $f(4)$ .

$f(4)=-4^{2} +4(4)+12\\f(4)=-16+16+12\\f(4)=12$

Also, replace $x=4$ in $g(x)=-x+6$ to obtain the value of $g(4)$ .

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Step 5:

Insert $x=5$ in $f(x)=-x^{2} +4x+12$ to obtain the value of $f(5)$ .

$f(5)=-5^{2} +4(5)+12\\f(5)=-25+20+12\\f(5)=7$

Replace $x=5$ in $g(x)=-x+6$ to find the value of $g(5)$ .

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Step 6:

Insert $x=6$ into $f(x)=-x^{2} +4x+12$ to find the value of $f(6)$ .

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According to the provided condition $f(x)=g(x)$ .

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The table representing function $f(x)=-x^{2} +4x+12$ and $g(x)=-x+6$ is included below.

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