Delaney would like to make a 10 lb nut mixture that is 60% peanuts and 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.
(a) what is the system that models this solution?
(b) which of the following is a solution to the system: 4 lb peanuts and 6 lb mixture; 5 lb peanuts and 5 lb mixture; 8 lb peanuts and 2 lb mixture? show your work.

If there is "p" pounds of peanuts and "m" pounds of '20% peanuts and 80% almonds' mixture, then, we can get the following equations,

p + m = 10 -----------(1) and

4m/5 = 4 ------------(2)

whose solution is 5 lb peanuts and 5 lb mixture.

Step-by-step explanation:

In the mixture which Delaney wants to make there would be

lb

= 6 lb of peanuts

So, there will be (10 - 6) lb  

= 4 lb of almonds

If  Delaney has "p" pounds of peanuts and "m" pounds of the '20% peanuts and 80% almonds' mixture, then according to the question,

p + m = 10 -----------(1) and

4m/5 = 4 ------------(2)

So, from (2),

m = 5 --------------(3)

So, from (1) and (3) ,

p = (10 - 5) = 5  

let soccer = x and golf = y

part a

1st equation: x + y = 125

2nd equation: x = y +45

part b

replace x in the 1st equation with the 2nd one:

y + 45 + y = 125

simplify:

2y + 45 = 125

subtract 45 from each side:

2y = 80

divide both sides by 2:

y = 80/2

y = 40

she plays golf for 40 minutes.

part c

no because she plays soccer for 45 minutes longer than golf 40 +45 =   85 minutes, not 80 minutes.

the answer is 13

step-by-step explanation:

5*5=25

12*12=144

25+144=169

169^2=13