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Write a system of equations to describe the situation below, solve using any method, and fill in the blanks.The members of a sewing circle are making blankets to give to shelters. This week, they made twin-size blankets and queen-size blankets, using a total of meters of fabric. Last week, the members completed twin-size blankets and queen-size blankets, which required total meters of fabric. How much fabric is used for the different sizes of blankets?A twin-size blanket uses meters of fabric and a queen-size one uses meters.
Full solution
Q. Write a system of equations to describe the situation below, solve using any method, and fill in the blanks.The members of a sewing circle are making blankets to give to shelters. This week, they made twin-size blankets and queen-size blankets, using a total of meters of fabric. Last week, the members completed twin-size blankets and queen-size blankets, which required total meters of fabric. How much fabric is used for the different sizes of blankets?A twin-size blanket uses meters of fabric and a queen-size one uses meters.
- Denote fabric amounts: Let's denote the amount of fabric used for a twin-size blanket as meters and for a queen-size blanket as meters. We are given two situations to form our system of equations.
- First situation equation: From the first situation, we have the equation for this week's production: twin-size blankets and queen-size blankets used a total of meters of fabric.
- Second situation equation: From the second situation, we have the equation for last week's production: twin-size blankets and queen-size blankets used a total of meters of fabric.
- System of equations: We now have a system of equations:We can solve this system using either substitution or elimination. Let's use the elimination method.
- Elimination method: To eliminate one of the variables, we can multiply the first equation by and the second equation by to make the coefficients of the same.This gives us:
- Eliminate x: Now, we subtract the second equation from the first to eliminate x:
- Solve for y: Solve for y:So, each queen-size blanket uses meters of fabric.
- Substitute and solve for : Substitute the value of back into one of the original equations to solve for . We'll use the first equation:
- Substitute and solve for x: Substitute the value of back into one of the original equations to solve for . We'll use the first equation:Solve for :So, each twin-size blanket uses meters of fabric.
