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
The trail mix has :
[tex]\frac{2}{3}[/tex] pounds of almonds
[tex]\frac{4}{3}[/tex] pounds of coffee beans
2 pounds of peanuts.
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.
[tex]12x+9y+5z=30[/tex] .... (1)
[tex]2x=y[/tex]
[tex]3x=z[/tex]
Substituting in equation 1
[tex]12x+9(2x)+5(3x)=30[/tex]
[tex]12x+18x+15x=30[/tex]
[tex]45x=30[/tex]
[tex]x=\frac{2}{3}[/tex] pounds (almonds)
Now, y = 2x, so y = [tex]\frac{4}{3}[/tex] pounds (coffee beans)
And z = 3x, so z = 2 pounds (peanuts)
Now checking the amounts:
Almonds : [tex]12*\frac{2}{3}= 8[/tex] dollars
Coffee beans : [tex]9*\frac{4}{3}=12[/tex] dollars
Peanuts : [tex]5*2=10[/tex] dollars
Total amount = [tex]8+12+10=30[/tex] dollars
Therefore, the trail mix has :
[tex]\frac{2}{3}[/tex] pounds of almonds
[tex]\frac{4}{3}[/tex] pounds of coffee beans
2 pounds of peanuts.
