A balloon lifts off the ground and reaches a height of 200m. The total mass of the balloon is 1000 kg. What is the GPE of the ba
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Answer:
The price of one pound of coffee is 32 pesos
The price of one pound of sugar is 7 pesos
Step-by-step explanation:
The question in English is
6 pounds of coffee and 5 pounds of sugar cost 227 pesos and 5 pounds of coffee and 4 pounds of sugar (at the same prices) cost 188 pesos Find the price of one pound of coffee and one pound of sugar.
Let
x-----> the price of one pound of coffee
y-----> the price of one pound of sugar
we know that
6x+5y=227 -----> equation A
5x+4y=188 ----> equation B
Solve the system of equations by graphing
Remember that the solution of the system of equations is the intersection point both graphs
The solution is the point (32,7)
see the attached figure
therefore
The price of one pound of coffee is 32 pesos
The price of one pound of sugar is 7 pesos
Answer:
1. <u>Cost per customer</u>: 10 + x
<u>Average number of customers</u>: 16 - 2x
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>:
<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:
Find the roots by equating to zero:
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:
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>:
Therefore, the possible buffet prices Noah could charge are:
$10, $11, $12 and $13.