Mr stephens needs to haul 1,518 tons of rocks from a construction site. his dump truck can hold 26 ton per load. how many tons will mr. stephens need to haul in the last load to move all of the rocks?

10

Step-by-step explanation:

1518 divided by 26 is 58 remainder 10.

... 1518 = 26×58 + 10 = 1508 + 10

Mr. Stephens will make 58 trips with a full load. After that, 10 tons of rock will remain.

delaney would like to make a 5lb 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.

:

p + m = 5

therefore

m = (5-p)

write an equation based on the percent of peanuts

1p + .2m = .6(5)

replace m with (5-p)

p + .2(5-p) = .6(5)

p + 1 - .2p = 3

p - .2p = 3 - 1

.8p = 2

p = 2/.8

p = 2.5 lbs of peanuts required

then

5 - 2.5 = 2.5 lbs of the peanut/almond mixture required

:

a) what is the system that models this situation?

p + m = 5

1p + .2m = .6(5)

2.14x - 12.18 = -5.76

add 12.18 to each side

2.14x -12.18 +12.18 = -5.76 +12.18

2.14 x =6.42

divide by 2.14

2.14x/2.14 = 6.42/2.14

x=3