Pecans sells for $3.50 a pound. Almonds sells for $5 pound. How many pounds of each should be used to make 15 pounds of mixture that sells for $4 a pound?
c+e=5
$3.50c+15e=5(4)
this is a mixture problem
Let P be the pounds of Pecans
and A be the pounds of almonds.
P+A=15 (given)
now, the cost: 3.5*P is the cost of pecans, and 5*A is the cost of almonds, then the sum of costs equals total cost.
3.5P+5A=4*15
So now, you know A=15-P so
3.5P+5(15-P)=4*15 and you solve for P, pounds of Pecans. Then go back and solve for A, since A=15-P
To solve this problem, we can use a system of equations to represent the given information. Let's assign variables to the unknown quantities:
Let's say x represents the number of pounds of pecans used.
Let's say y represents the number of pounds of almonds used.
From the given information, we can set up the following equations:
1) The total weight of the mixture is 15 pounds:
x + y = 15
2) The cost of the mixture is $4 per pound:
(3.50x + 5y) / 15 = 4
Now, we can solve this system of equations to find the values of x and y.
To eliminate decimals, we can multiply both sides of equation 2 by 15 to get rid of the denominator:
3.50x + 5y = 60
Now we have a system of equations:
x + y = 15
3.50x + 5y = 60
We can solve this system using various methods, such as substitution or elimination. Here, let's use the method of substitution.
From equation 1, we know that x = 15 - y. Substituting this value of x into equation 2, we can solve for y:
3.50(15 - y) + 5y = 60
52.50 - 3.50y + 5y = 60
52.50 + 1.50y = 60
1.50y = 7.50
y = 7.50 / 1.50
y = 5
Now that we have the value of y, we can substitute it back into equation 1 to find the value of x:
x + 5 = 15
x = 15 - 5
x = 10
So, you should use 10 pounds of pecans and 5 pounds of almonds to make a 15-pound mixture that sells for $4 a pound.