Kimberly wants to make a mix of nuts and raisins for a party. Nuts cost $.20/oz and raisins cost $0.12/0z.
How many ounces of each should she buy if she wants 48 oz of mix that cost $0.15/oz
N+R=48
.2N+.12R=.15
solve. Does that help? Sounds like a lot of raisins...
Well, first of all, I have to commend Kimberly for having such nutty ambitions! Now, let's crunch some numbers to help her out.
Let's assume she buys x ounces of nuts and y ounces of raisins. Since she wants a total of 48 oz of mix, we know that x + y = 48.
Now, let's tackle the costs. She wants a mix that costs $0.15/oz, so the total cost of the nuts and raisins combined will be (x * $0.20) + (y * $0.12) = 48 * $0.15.
Simplifying that equation, we get 0.20x + 0.12y = 7.20.
Now, we have a system of equations to solve. But instead of doing that, let's have some fun with it! Throw a nut at one equation and see what sticks!
Let's multiply the first equation by 0.20 to get 0.20x + 0.20y = 9.60.
Now, subtract this new equation from the second one, and you'll see that the nuts cancel each other out. It's like a nut fight! What's left is: 0.20x + 0.12y - 0.20x - 0.20y = 7.20 - 9.60.
Simplifying further, we get -0.08y = -2.40.
No worries, though! Divide both sides by -0.08, and you'll find that y = 30.
Now, substitute y back into the first equation: x + 30 = 48. Solve for x, and you'll see that x = 18.
So, Kimberly should buy 18 oz of nuts and 30 oz of raisins to achieve her nutty mix for the party!
Let's assume Kimberly buys x ounces of nuts and y ounces of raisins.
Since she wants a total of 48 oz of the mix, we can write the equation:
x + y = 48 -- Equation 1
The cost per ounce of the mix is $0.15. So the total cost of the mix is:
0.15 * 48 = $7.20
The cost of nuts per ounce is $0.20, so the total cost of the nuts is:
0.20x
The cost of raisins per ounce is $0.12, so the total cost of the raisins is:
0.12y
Since the total cost of the mix is $7.20, we can write the equation:
0.20x + 0.12y = 7.20 -- Equation 2
Now, we can solve the system of equations (Equation 1 and Equation 2) to find the values of x and y.
Multiplying Equation 1 by 0.12 to match the coefficient of y in Equation 2, we get:
0.12x + 0.12y = 5.76 -- Equation 3
Now subtract Equation 3 from Equation 2 to eliminate the y term:
(0.20x + 0.12y) - (0.12x + 0.12y) = 7.20 - 5.76
Simplifying, we get:
0.08x = 1.44
Dividing both sides by 0.08, we get:
x = 18
Substituting the value of x in Equation 1, we can find the value of y:
18 + y = 48
Simplifying, we get:
y = 48 - 18
y = 30
Therefore, Kimberly should buy 18 ounces of nuts and 30 ounces of raisins to make a 48 oz mix that costs $0.15/oz.
To determine how many ounces of nuts and raisins Kimberly should buy, we need to set up a system of equations based on the given information.
Let's assume x is the number of ounces of nuts and y is the number of ounces of raisins.
The total weight of the mix is given as 48 oz, so the first equation is:
x + y = 48
The cost per ounce of the mix is given as $0.15. So, the second equation is:
(0.20 * x) + (0.12 * y) = 0.15 * 48
Now, we can solve this system of equations to find the values of x and y.
To solve the system of equations, we can use substitution or elimination method. In this case, let's use substitution:
From the first equation, we can isolate x:
x = 48 - y
Substituting this value of x into the second equation, we have:
(0.20 * (48 - y)) + (0.12 * y) = 0.15 * 48
Simplifying this equation:
9.6 - 0.2y + 0.12y = 7.2
Combining like terms:
-0.08y = 7.2 - 9.6
-0.08y = -2.4
Dividing both sides by -0.08:
y = -2.4 / -0.08
y = 30
Now, we can substitute this value of y back into the first equation to find x:
x = 48 - y
x = 48 - 30
x = 18
Thus, Kimberly should buy 18 ounces of nuts and 30 ounces of raisins to make a mix of 48 ounces that costs $0.15 per ounce.