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olya-2409 [2.1K]
3 years ago
15

A store is selling a mixture of apple granola and blueberry granola for $6.99 per pound. Blueberry granola costs $8.99 per pound

and apple granola costs $5.99. How many pounds of each should be used to make 30 pounds of mixture?
Mathematics
1 answer:
Alik [6]3 years ago
7 0

Answer:the number of pounds of blueberry granola that she should put in the mixture is 10 pounds.

the number of pounds of apple granola that she should put in the mixture is 20 pounds

Step-by-step explanation:

Let x represent the number of pounds of blueberry granola that she should put in the mixture.

Let y represent the number of pounds of apple granola that she should put in the mixture.

She wants to make a 30 pounds mixture. This means that

x + y = 30

A store is selling a mixture of apple granola and blueberry granola for $6.99 per pound. This means that the cost of the 30 pound mixture would be

30 × 6.99 = $209.7

Blueberry granola costs $8.99 per pound and apple granola costs $5.99. This means that

8.99x + 5.99y = 209.7 - - - - - - - - - -1

Substituting x = 30 - y into equation 1, it becomes

8.99(30 - y) + 5.99y = 209.7

269.7 - 8.99y + 5.99y = 209.7

- 8.99y + 5.99y = 209.7 - 269.7

- 3y = - 60

y = - 60/ -3

y = 20

Substituting y = 20 into x = 30 - y, it becomes

x = 30 - 20 = 10 pounds

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The division of whole numbers is commutative. true or false?
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3 years ago
A tank is filled at a constant rate. 10 minutes after filling is started, the tank contains 4.8L of water. After 35 minutes the
Mashcka [7]

Answer:

Part A)

0.1 liters per minute.

Part B)

There was initially 3.8 liters of water.

\displaystyle V(t) = 0.1(t - 10) + 4.8

Part C)

562 minutes.

Step-by-step explanation:

A tank is filled at a constant rate. After 10 minutes, the tank contains 4.8 L of water and after 35 minutes, the tank contains 7.3 L of water.

Part A)

We can represent the current data with two points: (10, 4.8) and (35, 7.3). The <em>x-</em>coordinate is measured in minutes since the tank began to be filled and the <em>y-</em>coordinate is measured in how full the tank is in liters.

To find the rate at which the tank is being filled, find the slope between the two points:

\displaystyle m = \frac{\Delta y}{\Delta x} = \frac{(7.3)-(4.8)}{(35)-(10)} = \frac{2.5}{25} = 0.1

In other words, the rate at which the tank is being filled is 0.1 liters per minute.

Part B)

To find the function of the volume of the tank, we can use the point-slope form to first find its equation:

\displaystyle y - y_1 = m( x - x_1)

Where <em>m</em> is the slope/rate of change and (<em>x</em>₁, <em>y</em>₁) is a point.

We will substitute 0.1 for <em>m</em> and let (10, 4.8) be the point. Hence:

\displaystyle y - (4.8) = 0.1(x - 10)

Simplify:

\displaystyle y = 0.1(x-10) + 4.8

Since <em>y</em> represent how full the tank is and <em>x</em> represent the time in minutes since the tank began to be filled, we can substitute <em>y</em> for V(t) and <em>x</em> for <em>t</em>. Thus, our function is:

<em />\displaystyle V(t) = 0.1(t - 10) + 4.8<em />

<em />

The initial volume is when <em>t</em> = 0. Evaluate:

\displaystyle V(0) = 0.1 ((0) - 10) + 4.8 = 3.8

There was initially 3.8 liters of water.

Part C)

To find how long it will take for the tank to be completely filled given its maximum capacity of 60 liters, we can let V(t) = 60 and solve for <em>t</em>. Hence:

60 = 0.1(t - 10) + 4.8

Subtract:

55.2 = 0.1(t - 10)

Divide:

552 = t - 10

Add. Therefore:

t = 562\text{ minutes}

It will take 562 minutes for the tank to be completely filled.

8 0
2 years ago
30 POINTSSS!!!!
NARA [144]
The answers are B and C
3 0
3 years ago
Read 2 more answers
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