Write an article based on this "Determine the two "ingredients. Fill out the first column of your chart. Fill out the second column of your chart. Fill out the third column of your chart. Set up the equation. Solve the equation. Find the missing amounts of each ingredient."
" These will be two items that are being combined. They might be food ingredients, or differently priced items, such as tickets. For example, you might be trying to solve the following problem: The student council is selling 100 cups of punch at a school dance. The punch is made from a combination of fruit juice and lemon-lime soda. They want to sell each cup of punch for $1.00. Normally they would sell a cup of fruit juice for $1.15 and a cup of lemon lime soda for $0.75. How many cups of each ingredient should the student council use to make the punch? In this problem, fruit juice and lemon-lime soda are the two ingredients. The first column will be the amount of each ingredient in the final mixture, and the total amount of the mixture. You will likely need to use variables. For example, since you know the student council plans on making 100 cups of punch, you would write 100 in the third row of the first column. For the fruit juice, you would write the variable x{\displaystyle x}, since you don't know how much fruit juice will be in the final mixture. For the lemon-lime soda, you would write 100x{\displaystyle 100-x}, since the amount will be the difference between the amount of the total mixture and the amount of the other ingredient. This will be the unit price of each ingredient in the mixture, and the unit price of the mixture. For example, you know that the punch will be sold for $1.00 per cup, so write a 1 in the second column for the mixture. The fruit juice sells for $1.15 per cup, so write 1.15 in the second column for this ingredient. The soda sells for $0.75 per cup, so write 0.75 in the second column for lemon-lime soda. This column will represent the total price of each ingredient in the total mixture, as well as the total price of the mixture. To calculate this, multiply the values in the first and second column for each ingredient. For example, since 100 cups of punch will be made, and each cup will cost $1.00, the total price of the punch is 1001=100{\displaystyle 100 imes 1=100}. Since there are x{\displaystyle x} cups of fruit juice in the punch, and fruit juice is priced at $1.15 per cup, the total price of the fruit juice in the mixture is 1.15x{\displaystyle 1.15x}. Since there are 100x{\displaystyle 100-x} cups of soda in the punch, and soda is priced at $0.75 per cup, the total price of the soda in the mixture is 0.75(100x){\displaystyle 0.75(100-x)}. Simplified using the distributive property, this becomes 75.75x{\displaystyle 75-.75x}. To solve for x{\displaystyle x} set up an equation using the third column of the table. The values in the first and second row of the third column will add up to the value in the third row of the third column. For example, (1.15x)+(75.75x)=100{\displaystyle (1.15x)+(75-.75x)=100}. To do this, isolate the variable using normal algebra rules. Remember to balance the equation by completing calculations to both sides. For example, to solve for x{\displaystyle x}, you would first combine like x{\displaystyle x} terms, then subtract 75 from both sides of the equation, then divide both sides .4:(1.15x)+(75.75x)=100{\displaystyle (1.15x)+(75-.75x)=100}(1.15x.75x)+(75)=100{\displaystyle (1.15x-.75x)+(75)=100}.4x+75=100{\displaystyle .4x+75=100}.4x+7575=10075{\displaystyle .4x+75-75=100-75}.4x=25{\displaystyle .4x=25}.4x.4=25.4{\displaystyle {
rac {.4x}{.4}}={
rac {25}{.4}}}x=62.5{\displaystyle x=62.5} To do this, plug the value of x{\displaystyle x} into the table, and complete any necessary calculations. For example, since x=62.5{\displaystyle x=62.5}, the student council should use 62.5 cups of fruit juice in its punch, and 10062.5{\displaystyle 100-62.5}, or 37.5, cups of lemon-lime soda in the punch.