1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
Whitepunk [10]
4 years ago
13

1. Stephanie would like to make a 5 lb nut mixture that is 60% peanuts and 40% almonds. She has several pounds of peanuts and se

veral 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.
(a) What is the system that models this situation?
(b) 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 all your work.
Mathematics
1 answer:
Crazy boy [7]4 years ago
7 0
Answers:

(a) p + m = 5
     0.8m = 2

(b) 2.5 lb peanuts and 2.5 lb mixture

Explanations:

(a) Note that we just need to mix the following to get the desired mixture:

     - peanut (p) - peanuts whose amount is p
     - mixture (m) - mixture (80% almonds and 20% peanuts) that has an amount of m; we denote this as

By mixing the peanuts (p) and the mixture (m), we combine their weights and equate it 5 since the mixture has a total of 5 lb.

Hence, 

p + m = 5

Note that the desired 5-lb mixture has 40% almonds. Thus, the amount of almonds in the desired mixture is 2 lb (40% of 5 lb, which is 0.4 multiplied by 5).

Moreover, since the mixture (m) has 80% almonds, the weight of almonds that mixture is 0.8m.

Since we mix mixture (m) with the pure peanut to get the desired mixture, the almonds in the desired mixture are also the almonds in the mixture (m). 
So, we can equate the amount of almonds in mixture (m) to the amount of almonds in the desired measure.

In terms mathematical equation,

0.8m = 2 

Hence, the system of equations that models the situation is 

p + m = 5
0.8m = 2

(b) To solve the system obtained in (a), we first label the equations for easy reference,

(1) p + m = 5
(2) 0.8m = 2

Note that using equation (2), we can solve the value of m by dividing both sides of (2) by 0.8. By doing this, we have

m = 2.5

Then, we substitute the value of m to equation (1) to solve for p:

p + m = 5
p + 2.5 = 5   (3)

To solve for p, we subtract both sides of equation (3) by 2.5. Thus,

p = 2.5

Hence, 

m = 2.5, p = 2.5

Therefore, the solution to the system is 2.5 lb peanuts and 2.5 lb mixture.  







 
You might be interested in
A recipe requires 3 1/2 cups of milk. Sam put in 1 3/4 cups and emptied the container. How much more milk does she need to put i
s344n2d4d5 [400]

Answer:

1 3/4

Step-by-step explanation: you would add 1/4 to the 1 3/4 sam already put in. at that point your left with 2 cups and to get to 3 1/2 from 2 you need 1 1/2 cups

6 0
3 years ago
Read 2 more answers
You randomly choose one of the tiles. Without replacing the first tile, you choose a second tile. Find the probability of the co
densk [106]

Answer: I really don't know yet.

Step-by-step explanation:

Another day. 5^{2}

6 0
3 years ago
Solve the equation 9=8(n+4)-7
irga5000 [103]

Answer:

n= -2

Step-by-step explanation:

If you have any questions about the way I solved it, don't hesitate to ask ;)

6 0
3 years ago
0.1562 rounded to the nearest hundredth place
kondaur [170]

Answer:

0.16

Step-by-step explanation:

if the number in the thousandths is 5 or over you round it up.

3 0
3 years ago
Read 2 more answers
9/4 divided by 3/8= 9/4 x 8/3
erma4kov [3.2K]

Answer:

9/4:3/8=9/4×8/3=72/12=24/4=6/1=6

7 0
3 years ago
Read 2 more answers
Other questions:
  • Geometry math question no Guessing and Please show work thank you
    8·1 answer
  • A ________________________________ is a range of values within which it is probable that the true value of a parameter (e.g., a
    13·1 answer
  • Que son las figuras planas
    9·1 answer
  • What is formed by the intersection of a line and a plane if the line does not lie in the plane?
    9·1 answer
  • Lionel is planning a one-day outing
    7·1 answer
  • What is the value of h????
    9·1 answer
  • Meg bought 20 bags of candy for the party. If 2/5 of the bags are Skittles, how many bags of Skittles does she have?
    15·1 answer
  • Tanya has a $50 gift card to spend on Amazon. She wants an airpod case cover for $12.
    10·1 answer
  • 6/a - 4/b = 1 and 9/a - 8/b = 1​
    7·1 answer
  • I need help. I need help. I need help. I need help. I need help. I need help. I need help. I need help. I need help. I need help
    12·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!