A store is having a sale on walnuts and chocolate chips. For
3
pounds of walnuts and
2
pounds of chocolate chips, the total cost is
$11
. For
5
pounds of walnuts and
6
pounds of chocolate chips, the total cost is
$23
. Find the cost for each pound of walnuts and each pound of chocolate chips.
Chocolate chips:1.75
Walnuts: 2.50
5x + 3y =23
2x +12y =47
To find the cost per pound of walnuts and chocolate chips, we can set up a system of equations using the given information.
Let's call the cost per pound of walnuts "w" and the cost per pound of chocolate chips "c".
From the first statement in the problem, we know that 3 pounds of walnuts and 2 pounds of chocolate chips cost $11. We can write this as an equation:
3w + 2c = 11
Similarly, from the second statement, we know that 5 pounds of walnuts and 6 pounds of chocolate chips cost $23. We can write this as another equation:
5w + 6c = 23
To solve this system of equations, we can use the method of substitution or elimination. Let's use the method of substitution.
First, solve one equation for one variable in terms of the other variable. Let's solve the first equation for w:
3w + 2c = 11
3w = 11 - 2c
w = (11 - 2c) / 3
Now, substitute this expression for w into the second equation:
5w + 6c = 23
5((11 - 2c) / 3) + 6c = 23
Simplify this equation:
(55 - 10c) / 3 + 6c = 23
55 - 10c + 18c = 69
8c = 14
c = 14 / 8
c = 1.75
Now that we have the value for c, we can substitute it back into one of the original equations to find the value for w. Let's use the first equation:
3w + 2c = 11
3w + 2(1.75) = 11
3w + 3.5 = 11
3w = 11 - 3.5
3w = 7.5
w = 7.5 / 3
w = 2.5
Therefore, the cost per pound of walnuts is $2.50 and the cost per pound of chocolate chips is $1.75.
3w + 2c = 11
5w + 6c = 23
first times 3: 9w + 6c = 33
2nd as is : 5w + 6c = 23
subtract them:
4w = 10
w = 2.50
sub back into first to find c
6x+5y=23
2×+3y=11