A store is having a sale on chocolate chips and walnuts. For 3 pounds of chocolate chips and 5 pounds of walnuts, the total cost is $17. For 12 pounds of chocolate chips and 2 pounds of walnuts, the total cost is $23 . Find the cost for each pound of chocolate chips and each pound of walnuts.
To find the cost for each pound of chocolate chips and each pound of walnuts, we can set up a system of equations.
Let's assign variables to the unknowns:
Let x be the cost per pound of chocolate chips.
Let y be the cost per pound of walnuts.
From the given information, we can create two equations:
Equation 1: 3x + 5y = 17
This equation represents the total cost for 3 pounds of chocolate chips and 5 pounds of walnuts, which is $17.
Equation 2: 12x + 2y = 23
This equation represents the total cost for 12 pounds of chocolate chips and 2 pounds of walnuts, which is $23.
Now, we can solve this system of equations using substitution or elimination method.
Let's use the elimination method in this case:
Multiply equation 1 by 2 and equation 2 by 5 to create equivalent equations:
Equation 1': 6x + 10y = 34
Equation 2': 60x + 10y = 115
Now, subtract the equations to eliminate y:
(Equation 2') - (Equation 1'): (60x + 10y) - (6x + 10y) = 115 - 34
54x = 81
Divide both sides of the equation by 54:
54x/54 = 81/54
x = 3/2 = $1.50
Now, substitute the value of x into any of the original equations to find the value of y. Let's use equation 1:
3(1.50) + 5y = 17
4.50 + 5y = 17
5y = 17 - 4.50
5y = 12.50
Divide both sides of the equation by 5:
5y/5 = 12.50/5
y = 2.50
Therefore, the cost per pound of chocolate chips is $1.50, and the cost per pound of walnuts is $2.50.
3x + 5y = 17
12x + 2y = 23
and solve : )