Question

Krishna wants to make trail mix made up of almonds, chocolate covered coffee beans, and peanuts. He wants to mix one part almonds, two parts coffee beans, and three parts of peanuts. Almonds cost $12 per pound, coffee beans cost $9 per pound, and peanuts cost $5 per pound. Carlos has $30 to spend on the trail mix. How many pounds of trail mix he can make?

Answer 1

The trail mix has :

`(2)/(3)` pounds of almonds

`(4)/(3)` pounds of coffee beans

2 pounds of peanuts.

Explanation:

Given is :

1 part almond

2 parts coffee beans

3 parts peanuts

This can be written as 1:2:3

Cost of almond = 12 per pound

Cost of coffee beans = 9 per pound

Cost of peanuts = 5 per pound

Let x represents almonds

Let y represents coffee beans

Let z represent peanuts

Given is : Carlos has $30 to spend on the trail mix.

`12x+9y+5z=30` .... (1)

`2x=y`

`3x=z`

Substituting in equation 1

`12x+9(2x)+5(3x)=30`

`12x+18x+15x=30`

`45x=30`

`x=(2)/(3)` pounds (almonds)

Now, y = 2x, so y =
`(4)/(3)` pounds (coffee beans)

And z = 3x, so z = 2 pounds (peanuts)

Now checking the amounts:

Almonds :
`12*(2)/(3)= 8` dollars

Coffee beans :
`9*(4)/(3)=12` dollars

Peanuts :
`5*2=10` dollars

Total amount =
`8+12+10=30` dollars

Therefore, the trail mix has :

`(2)/(3)` pounds of almonds

`(4)/(3)` pounds of coffee beans

2 pounds of peanuts.

Answer 2

Answer: 4.02 pounds

Given: Krishna wants to make trail using the following ingredients:

one part almonds at $12/lb

two parts coffee beans at $9/lb

three parts of peanuts.at $5/lb

If Carlos has $30 to spend on the trail mix, the weight of the mixture is calculated below:

Let X=almonds in pounds

2X=coffee beans in pounds

3X=peanuts in pounds

X($12)+2x($9)+3X($5)=$30

12X+18x+15X=30

45X=30

X=30/45

X=.67 lbs

2X=1.34 lbs

3X=2.01 lbs

X+2X+3X=.67+1.34+2.01

Total weight of trail mix=4.02 pounds