Austin is creating a new trail mix by
combining two of his bestselling blends. A
pineapplecoconutmacadamia (pcm) mix
that sells for $18/kg and a bananapapayapeanut (bpp) mix that sells for $10/kg. Write
the equations and find the point of
intersection. He is making 80kg of the new mix and will sell it for $12.50/kg.
a) write 2 equations of the linear relations. I've already gotten the 2 equations. let x represent pcm and y represent bpp. so x+y= 80. the second equation is 18y+10y = 1000 ( multiplying $12.50x80=1000 )
b) how much blend will austin use? i need help on this part..
25 kg of pineapple mix and 55 kg of banana mix
sorry ignore " Write
the equations and find the point of
intersection." in the problem.
sorry, another typo, 18y should be 18x
please help, it's urgent. thanks
ms. sue i need your help
To find how much of each blend Austin will use, you need to solve the system of equations you wrote:
Equation 1: x + y = 80
Equation 2: 18x + 10y = 1000
To solve the system, you can use the substitution or elimination method. In this case, let's use the substitution method.
Step 1: Solve Equation 1 for x:
x = 80 - y
Step 2: Substitute the value of x in Equation 2:
18(80 - y) + 10y = 1000
Step 3: Simplify and solve for y:
1440 - 18y + 10y = 1000
1440 - 1000 = 18y - 10y
440 = 8y
y = 55
Step 4: Substitute the value of y back into Equation 1 to find x:
x + 55 = 80
x = 80 - 55
x = 25
So, Austin will use 25kg of the pineapple-coconut-macadamia (pcm) mix and 55kg of the banana-papaya-peanut (bpp) mix to create his new trail mix.
I hope this helps!