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Write a system of equations to describe the situation below, solve using elimination, and fill in the blanks.\newlineThe members of a sewing circle are making blankets to give to shelters. This week, they made 4848 twin-size blankets and 3838 queen-size blankets, using a total of 372372 yards of fabric. Last week, the members completed 4848 twin-size blankets and 2424 queen-size blankets, which required 288288 total yards of fabric. How much fabric is used for the different sizes of blankets?\newlineA twin-size blanket uses _\_ yards of fabric and a queen-size one uses _\_ yards.

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Q. Write a system of equations to describe the situation below, solve using elimination, and fill in the blanks.\newlineThe members of a sewing circle are making blankets to give to shelters. This week, they made 4848 twin-size blankets and 3838 queen-size blankets, using a total of 372372 yards of fabric. Last week, the members completed 4848 twin-size blankets and 2424 queen-size blankets, which required 288288 total yards of fabric. How much fabric is used for the different sizes of blankets?\newlineA twin-size blanket uses _\_ yards of fabric and a queen-size one uses _\_ yards.
  1. Define Variables: Let's denote the amount of fabric used for a twin-size blanket as xx yards and for a queen-size blanket as yy yards. We can write two equations based on the information given for this week and last week.
  2. Formulate Equations: This week's equation: 48x+38y=37248x + 38y = 372 (since 4848 twin-size and 3838 queen-size blankets used 372372 yards of fabric).
  3. Elimination Method: Last week's equation: 48x+24y=28848x + 24y = 288 (since 4848 twin-size and 2424 queen-size blankets used 288288 yards of fabric).
  4. Simplify Equation: To solve the system using elimination, we can subtract the second equation from the first to eliminate xx.(48x+38y)−(48x+24y)=372−288(48x + 38y) - (48x + 24y) = 372 - 288
  5. Solve for y: This simplifies to:\newline48x+38y−48x−24y=372−28848x + 38y - 48x - 24y = 372 - 288\newline14y=8414y = 84
  6. Substitute y Value: Now, divide both sides by 1414 to find the value of y:\newline14y14=8414\frac{14y}{14} = \frac{84}{14}\newliney=6y = 6
  7. Solve for x: Now that we have the value of yy, we can substitute it back into one of the original equations to find xx. Let's use the second equation:\newline48x+24(6)=28848x + 24(6) = 288
  8. Final Results: Substitute the value of yy into the equation: 48x+144=28848x + 144 = 288
  9. Final Results: Substitute the value of yy into the equation:\newline48x+144=28848x + 144 = 288Subtract 144144 from both sides to solve for xx:\newline48x=288−14448x = 288 - 144\newline48x=14448x = 144
  10. Final Results: Substitute the value of yy into the equation:\newline48x+144=28848x + 144 = 288Subtract 144144 from both sides to solve for xx:\newline48x=288−14448x = 288 - 144\newline48x=14448x = 144Now, divide both sides by 4848 to find the value of xx:\newline48x48=14448\frac{48x}{48} = \frac{144}{48}\newlinex=3x = 3
  11. Final Results: Substitute the value of yy into the equation:\newline48x+144=28848x + 144 = 288Subtract 144144 from both sides to solve for xx:\newline48x=288−14448x = 288 - 144\newline48x=14448x = 144Now, divide both sides by 4848 to find the value of xx:\newline48x48=14448\frac{48x}{48} = \frac{144}{48}\newlinex=3x = 3We have found that a twin-size blanket uses 48x+144=28848x + 144 = 28800 yards of fabric and a queen-size one uses 48x+144=28848x + 144 = 28811 yards.

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