Question

i need the equation. there are two hundred nuts in a can of mixed nuts including peanuts,cashews,almonds,and walnuts. there are twice as many peanuts as cashews, twenty more cashews then almonds, and ten fewer almonds then twice the number of walnuts how many of each nuts. please explain thanks!

Answer 1

let number of cahews = x
there are twice as many peanuts as cashews
so number of peanuts = 2x
there are twenty more cashews then almonds
so number of almonds = x-20

there are ten fewer almonds then twice the number of walnuts

let number of walnuts = y
so number of almonds = 2y-10

but also number of almonds = x-20 (as stated above)

so x-20 = 2y-10

so x=2y+10

now we have

number of cashwes = x = 2y +10
number of peanuts = 2x = 2(2y+10) (substituting value of x)
number of almonds = x-20 = (2y+10) -20
number of walnuts = y

all add up to 200

so 2y+10 + 2(2y+10) + (2y+10)-20 + y =200

solve the equation for y to get y=20

number of cashwes = x = 2y +10 = 2*20+10 = 50

number of peanuts = 2x = 2(2y+10) = 2(2*20+10) = 100

number of almonds = x-20 = (2y+10)-20 = (2*20 +10)-20 = 30

number of walnuts = y = 20