Find the simplest algebraic expression for the following situation.
Susie, Sarah, and Tamera are planning to knit sweaters for their family. The sweaters will be made with yellow and blue yarn.
Susie needs to order 5 skeins of yellow yarn and 3 skeins of blue yarn.
Sarah needs to order 12 skeins of yellow yarn and 4 skeins of blue yarn.
Tamera needs to order 8 skeins of yellow yarn and 10 skeins of blue yarn.
How much total yarn should be ordered?
5y + 4b + 12y + 4b + 8y + 10b = ?
Combine like terms and add.
To find the total amount of yarn that should be ordered, you can add up the number of skeins needed for each color. Let's assign variables to represent the number of skeins of yellow and blue yarn:
Let "y" represent the number of skeins of yellow yarn.
Let "b" represent the number of skeins of blue yarn.
Now we can write the expressions for the number of skeins each person needs:
Susie: 5 yellow yarn + 3 blue yarn = 5y + 3b
Sarah: 12 yellow yarn + 4 blue yarn = 12y + 4b
Tamera: 8 yellow yarn + 10 blue yarn = 8y + 10b
To find the total amount of yarn, we need to add up the expressions:
Total yarn = (5y + 3b) + (12y + 4b) + (8y + 10b)
Simplifying and combining like terms, we get:
Total yarn = 25y + 17b
So the simplest algebraic expression for the total amount of yarn that should be ordered is 25y + 17b.