ALGEBRA 1 HELPP!! Armand needs to buy more than 60 yards of fabric, in total to compare a art project.

Question

HE will buy x yards of cotton fabric and silk fabric. Cotton costs $5 per yard and silk costs $10 per yard. He can spend at most $400 Write 2 inequalities.

Answer 1

Hi Sara!

So let us break down this problem step-by-step!

Armand needs to buy more than 60 yards of fabric while can only spend up to $400 in total. He needs two types of fabrics: cotton and silk. Let us label the following as:

Cotton = "x" variable

Silk = "y" variable

The first inequality asks us to create the total amount (in yards) he can purchase. The key term here is "more than," which symbolizes that he needs more than 60; not at 60, but it can be 61 yards, 62 yards, etc. So we use the greater than symbol (>) below:

x+y > 60 <-- This means that the total of cotton and silk should add up to more than 60 yards.

The second inequality asks us to create the total amount he can spend on each type of fabric, but the total CANNOT exceed $400. The key term here is "at most," which refers to Armand spending around $400 for more than 60 yards of fabric. In this case, we use the less than or equal to a symbol (≤) below:

** For the cotton fabric, it costs $5 per yard, so the first term is 5x, and the silk fabric costs $10 per yard, so the second term is 10y. In total, this should add up to or close to $400.

5x+10y ≤ $400 <-- This will determine that once Armand calculates how much cotton and silk fabric he needs and as long as it is more than 60 yards in total, this inequality will help him figure out the total cost of all that fabric.

I hope this helps, and feel free to ask more questions!

Answer 2

x +.y > 60

5x + 10y ≤ 400