MATHEMATICS HIGH SCHOOL

Delaney would like to make a 5 lb nut mixture that is 60% peanuts and 40% almonds. She has several pounds of peanuts and several pounds of a mixture that is 20% peanuts and 80% almonds. Let p represent the number of pounds of peanuts needed to make the new mixture, and let m represent the number of pounds of the 80% almond-20% peanut mixture. What is the system that models this situation?

Which of the following is a solution to the system: 2 lb peanuts and 3 lb mixture; 2.5 lb peanuts and 2.5 lb mixture; 4 lb peanuts and 1 lb mixture? Show your work.

Answers

Answer 1
Answer:

Answer: The system that models this situation is:

{p+m=50.6p+0.2m=0.6×5​

This system can be solved by substitution or elimination. One possible solution is:

Multiply the second equation by 5 to eliminate the fractions:

{p+m=53p+m=15​

Subtract the first equation from the second equation to eliminate m:

2p=10

Solve for p:

p=210​=5

Substitute p into the first equation to find m:

m=5−p=5−5=0

The solution is (p, m) = (5, 0), which means Delaney needs 5 lb of peanuts and 0 lb of mixture.

Another possible solution is:

Multiply the first equation by -0.2 to eliminate m:

{−0.2p−0.2m=−10.6p+0.2m=3​

Add the two equations to eliminate m:

0.4p=2

Solve for p:

p=0.42​=5

Substitute p into the first equation to find m:

m=5−p=5−5=0

The solution is (p, m) = (5, 0), which means Delaney needs 5 lb of peanuts and 0 lb of mixture.

Therefore, the only correct option among the given choices is 4 lb peanuts and 1 lb mixture.

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Johanna is mixing red and blue paint to make purple paint for her bedroom. the amount of red paint and blue paint she needs is directly proportional to each other. if she uses three pints of blue paint and five pints of red paint, it makes the perfect shade of purple to match her bed comforter. johanna wants to make one more batch of purple paint in the exact same shade. if she only has 15 pints of red paint left, how much blue paint does she need?

Answers

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3 blue x 3=9 blue
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so she will need 9 pints of blue paint.

The scoop of an excavator holds 27 ft3 of sand. If the capacity of a freight car is 40 tons of sand and we know that 1 ft3 of sand weighs 0.5 tons, how many freight cars can be filled with 120 loads?

Answers

27ft³=x tons
1ft³=0.5 tons

(27cubicfeet)/(x_t_o_n_s) = (1cubic foot)/(0.5 tons)

Cross multiply
1x=13.5tons
x=13.5tons

So one scoop/load carries 13.5 tons of sand. Lets see how many 120 loads can carry.

13.5tons*120loads=1620 tons of sand

Now lets see how freight cars it would take to hold 1620 tons of sand

1620/40=40.5 freight cars

Since you can't have .5 of a freight car, lets round 40.5 up to 41

Answer=41 freight cars

Answer:

40.5

Step-by-step explanation:

Which size ice cream dessert gives you the best price per ounce? Small 6-oz for $2.49. Medium 10-oz cup for $3.49. Large 16-oz cup for $4.99. Or Super size 24-oz cup for $7.69.

Answers

Answer:

The large size gives the lowest price per ounce of 3.11875, therefor the best in terms of price

Step-by-step explanation:

Step 1: Determine expression for price per ounce

The expression for the total price of an ice cream dessert is as follows;

T=p×n

where;

T=total price of ice cream

p=price per ounce of ice cream

n=number of ounces of ice cream

Step 2: Convert total price to price per ounce

The expression can be rewritten as;

p=T/n

1. For small 6 ounce at $2.49, T=2.49, n=6-oz

p=2.49/6=0.415

The price per ounce of the small ice cream dessert=$0.415 per ounce

2. For the Medium 10-oz for $3.49, T=$3.49, n=10-oz

p=3.49/10=0.349

The price per ounce of the medium ice cream dessert=$0.349 per ounce

3. For the Large 16-oz for $4.99, T= $4.99, n=16

p=4.99/16=$0.311875

The price per ounce of the medium ice cream dessert=$0.311875 per ounce

4. For the super size 24-oz for $7.69, T=$7.69, n=24

p=7.69/24=0.32

The price per ounce of the super size cup is 0.32 per ounce

The large size gives the lowest price per ounce of 3.11875, therefor the best in terms of price

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Answers

Answer:

yo

Step-by-step explanation:

i hate pie

Answer:

u want us to calculate all that??  da-mn

Step-by-step explanation:

How can you choose values for x when making a table of values representing a real world situation?

Answers

You'll see how to set up a table, choose appropriate x-values, plug those values into the equation.

How many solutions does this system have?Y = x + 5
Y = -5x – 1
A) One
B) None
C) Infinite
D) Two

Answers

Well this does take some work on scratch paper but ill let you know that we have to plug these in to make one whole big equation 
lets do that!
x + 5 = -5x - 1 now add +1 to both sides of the equation 
   + 1 =       +1 it cancels out on the right side and we solve on the left 
*****************
x + 6 = -5x  Now lets subtract that(1x) from both sides 
-1x    = -1x ( if x stands alone, theres always an imaginary 1 right by it)
**************  now -5 - 1 = -6 so its -6x 
 6     =  -6x  Now divide both sides by -6 to isolate x to be alone 
÷-6   =  ÷6  It cancels out on the right side and we solve on the left
************ 6 ÷ -6 = 0  so lets see what we have 
 0    =   x 
Since zero is still a number this means there is only 1 solution!
Answer = A.) one 
I hope this helps! 
and dont forget 2 
MARK ME BRIANLIEST! 
=)
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