While working at The Nut House you are asked to make a mixture of raisins and nuts worth $2.75/lb. You have 12 pounds of raisins worth $1.25/lb. How many pounds of nuts worth $4.00/lb should you add to the raisins to get the right-priced mix?
I have no idea how to solve this. I am terrible at word problems.
first we represent the unknown using variable,
let x = pounds of nuts needed
then we set up equation. since we are given the number of pounds of raisins and its price per pound, we'll multiply it to get the total amount of the 12-lb raisins. we do the same for the the nuts,, this time we multiply x by the price of nut per pound which is 4 :
12*1.25 + 4x = 2.75*(12+x)
note that we multiply 2.75 by 12+x since mixture of nut and raisin,, solving for x,
15 + 4x = 33 + 2.75x
4x - 2.75x = 33 - 15
1.25x = 18
x = 14.4 lb of nuts
hope this helps~ :)
21
No worries! Word problems can be tricky, but I'll walk you through the steps to solve this one.
To find out how many pounds of nuts you need to add to the raisins, we first need to determine the cost per pound of the mixture.
Let's start by calculating the total cost of the raisins. You have 12 pounds of raisins worth $1.25/lb, so the total cost of the raisins is:
12 pounds * $1.25/pound = $15.00
Now, let's assume you're adding x pounds of nuts. The cost per pound of the nuts is $4.00/lb. Therefore, the total cost of the nuts would be:
x pounds * $4.00/pound = $4x
To find the total cost of the mixture, we just need to add the costs of the raisins and nuts. The total cost of the mixture should be $2.75/lb.
So, the equation for the total cost of the mixture is:
$15.00 (cost of raisins) + $4x (cost of nuts) = $2.75 (cost of mixture) * (12 pounds + x pounds)
Now, we can solve this equation to find the value of x, which represents the number of pounds of nuts to add to the raisins.
$15.00 + $4x = $2.75 * (12 + x)
Let's solve for x:
$15.00 + $4x = $33.00 + $2.75x
Combine like terms:
$4x - $2.75x = $33.00 - $15.00
$1.25x = $18.00
Now, divide both sides of the equation by $1.25 to isolate x:
x = $18.00 / $1.25
x = 14.4
So, you would need to add approximately 14.4 pounds of nuts worth $4.00/lb to the 12 pounds of raisins to get the right-priced mix.