When the polynomial:

A restaurant uses 4.375 pounds of cheese for every pizzas. At this rate, how many pounds of cheese are used per pizza?

faltersainse [42]

Complete Question:

A restaurant uses 4.375 pounds of cheese every 8 and 3/4 pizzas. At this rate how many pounds of cheese are used per pizza?

Answer:

0.5 pounds of cheese are used per pizza

Solution:

Given that,

A restaurant uses 4.375 pounds of cheese every 8 and 3/4 pizzas

Therefore,

$4.375\ pounds = 8\frac{3}{4}\ pizza \\\\4.375\ pounds = \frac{35}{4}\ pizza$

We have to find pounds used per pizza

Let "x" be the pounds used per pizza

Then,

$4.375\ pounds = \frac{35}{4}\ pizza \\\\x\ pounds = 1\ pizza$

By cross multiplying,

$4.375 \times 1 = x \times \frac{35}{4} \\\\x = 0.5$

Thus, 0.5 pounds of cheese are used per pizza

8 0

3 years ago

How to answer this? A farmer had 455 ducks and chickens. He sold 2/5 of the ducks and bought another 104 chickens. As a result,

julia-pushkina [17]

Answer:

(a) 25

(b) $4816

Step-by-step explanation:

Let's say the starting amount of ducks is d, and the starting amount of chickens is c. Since there are only ducks and chickens, we can say that d + c= 455.

Next, the farmer sells 2/5 of the ducks, so we subtract 2/5 of the ducks so that the ending duck amount is d - (2/5)d = (3/5) d

After that, the farmer buys another 104 chickens, so we add 104 chickens to the current amount of chickens to get the ending chicken number as 104+c

Given the ending duck and chicken count, we can say that the ending farm animal count (we can represent this as a) is (3/5)d + 104 + c = a

The number of ducks is 2/3 the total number of animals at the end, so (3/5)d = (2/3)a

Let's list our equations out so it is easier to solve:

d+c = 455

(3/5)d + 104 + c = a

(3/5)d = (2/3)a

We have three equations and need to solve for three variables. One common variable in all three equations is d, so it might help if we put everything in terms of d.

Starting with d+c=455, if we subtract d from both sides, we get c=455-d. We can substitute this in the second equation to get

(3/5)d + 104 + 455 - d = a

-(2/5)d + 559 = a

(3/5)d = (2/3)a

Next, we can substitute for a. If we multiply both sides by 3 and then divide by 2 in (3/5)d = (2/3)a , we get

(9/10)d = a

Substitute that in to the second equation to get

-(2/5)d + 559 = (9/10) d

-(4/10)d + 559 = (9/10) d

add (4/10)d to both sides to isolate the variable and its coefficient

(13/10)d = 559

multiply both sides by (10/13) to isolate the coefficient

d = 430

Therefore, the starting number of ducks is 430 and the starting amount of chickens is 455-430 = 25

For (b), 2/5ths of the ducks are sold, so this is (430) * (2/5) = 172. Each duck is sold for 28 dollars, so this is 172*28=$4816 as the total price

7 0

2 years ago

7x-2y=16 11x+6y=32.3 how to solve this math problem

Aneli [31]

Answer:

Step-by-step explanation:

These types of equations are called simultaneous equations and the method we can use to solve these type of equations is either Substitution, Elimination and Graphing.

We use substitution here because it is easier.

Equation 1

$7x-2y=16$

Equation 2

$11x+6y=32.3$

Lets take equation 1

$7x-2y=16\\7x=16+2y\\x=\frac{16+2y}{7}$

This is our equation 3 , now put it inside equation 2.

$11x+6y=32.3\\11(\frac{16+2y}{7} )+6y=32.3\\\frac{176+22y}{7} +6y=32.3\\\frac{176+22y+42y}{7}=32.3\\176+22y+42y=226.1 \\\\42y+22y=226.1-176\\64y=50.1\\y=\frac{50.1}{64} \\y=0.783\\$

We found the value of y , now to find the value of x insert the value of y in equation 3

$x=\frac{16+2y}{7}\\x=\frac{16+2(0.783)}{7} \\x=\frac{16+1.566}{7}\\x=\frac{17.566}{7}\\x=2.509$

Solved ! See the attached image on both the straight line graphs i have attached for better understanding. Where both the lines intersect each other is our value of (x , y) respectively.

6 0

2 years ago

Ryan bought a bike for $47,000 in the year 2002. Its value depreciates by 2% per year. What is the value

AleksAgata [21]

Answer:

$43351.30

Step-by-step explanation:

5 0

3 years ago

What is the equation of a line, in general form, that passes through point (1, -2) and has a slope of 1/3.

Rus_ich [418]

Answer: -1/3

Step-by-step explanation:

correct me if im wrong

8 0

3 years ago