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boyakko [2]
3 years ago
10

Minny has two coupons, but can use one of them. The first one is for $5 off an item; the second coupon is for 20% off an item. T

he product she is buying costs $28.
Part A: Which coupon should she use ?

Part B: How much money will she save by using the better coupon?
Mathematics
1 answer:
joja [24]3 years ago
5 0
Let's first solve for the $5 off coupon,

28 - 5 = 23

The final total is $23.00 with $5 off.

- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -

Now for the final price of the 20% off coupon,

20\% = 0.2

0.2 or 0.20 is decimal form of 20%. Easier to multiply than in percent form!

0.2 \times 28 = 5.6

$5.6 or $5.60 is 20% of 28, we're not done yet!

Lastly, subtract 20% off of 28 (5.6) from 28,

28 - 5.6 = 22.4
$22.4 or $22.40 is the final after 20% off!

- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -

Q. Which is less after the discounts??

$23.00 or $22.40

A. $22.40 of course which was the 20% off.

Part A : Which coupon should she use ?

Answer : Well, to get a lower price, less to pay, the 20% off coupon is better!

Part B: How much money will she save by using the better coupon?

Answer : $5.6 / $5.60 is the amount she'll save!

- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -

I hope that helps you out!!

Any more questions, please just ask me!!

~ Zoey
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Answer:

1.   <u>Cost per customer</u>:  10 + x

     <u>Average number of customers</u>:  16 - 2x

\textsf{2.} \quad  -2x^2-4x+160\geq 130

3.    $10, $11, $12 and $13

Step-by-step explanation:

<u>Given information</u>:

  • $10 = cost of buffet per customer
  • 16 customers choose the buffet per hour
  • Every $1 increase in the cost of the buffet = loss of 2 customers per hour
  • $130 = minimum revenue needed per hour

Let x = the number of $1 increases in the cost of the buffet

<u>Part 1</u>

<u></u>

<u>Cost per customer</u>:  10 + x

<u>Average number of customers</u>:  16 - 2x

<u>Part 2</u>

The cost per customer multiplied by the number of customers needs to be <u>at least</u> $130.  Therefore, we can use the expressions found in part 1 to write the <u>inequality</u>:

(10 + x)(16 - 2x)\geq  130

\implies 160-20x+16x-2x^2\geq 130

\implies -2x^2-4x+160\geq 130

<u>Part 3</u>

To determine the possible buffet prices that Noah could charge and still maintain the restaurant owner's revenue requirements, solve the inequality:

\implies -2x^2-4x+160\geq 130

\implies -2x^2-4x+30\geq 0

\implies -2(x^2+2x-15)\geq 0

\implies x^2+2x-15\leq  0

\implies (x-3)(x+5)\leq  0

Find the roots by equating to zero:

\implies (x-3)(x+5)=0

x-3=0 \implies x=3

x+5=0 \implies x=-5

Therefore, the roots are x = 3 and x = -5.

<u>Test the roots</u> by choosing a value between the roots and substituting it into the original inequality:

\textsf{At }x=2: \quad -2(2)^2-4(2)+160=144

As 144 ≥ 130, the <u>solution</u> to the inequality is <u>between the roots</u>:  

-5 ≤ x ≤ 3

To find the range of possible buffet prices Noah could charge and still maintain a minimum revenue of $130, substitute x = 0 and x = 3 into the expression for "cost per customer.  

[Please note that we cannot use the negative values of the possible values of x since the question only tells us information about the change in average customers per hour considering an <em>increase </em>in cost.  It does not confirm that if the cost is reduced (less than $10) the number of customers <em>increases </em>per hour.]

<u>Cost per customer</u>:  

x =0 \implies 10 + 0=\$10

x=3 \implies 10+3=\$13

Therefore, the possible buffet prices Noah could charge are:

$10, $11, $12 and $13.

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