Answer :
Sabrina has 4 spools of 3 yards, 5 spools of 5 yards, and 3 spools of 8 yards.
Sabrina has a total of 12 spools of ribbon, with each spool containing either 3 yards, 5 yards, or 8 yards of ribbon. The total length of ribbon she has is 68 yards. To determine how many spools of each length of ribbon she has, we need to use a system of equations since we have three unknown variables representing the number of spools for each ribbon length (let's denote them as x for 3 yards, y for 5 yards, and z for 8 yards).
First, we have the equation for the total number of spools:
- x + y + z = 12
Next, we have the equation for the total yards of ribbon:
- 3x + 5y + 8z = 68
Now we have two equations and three unknowns, but as we're dealing with whole spools, we can enumerate possibilities and check which combination of spools fits both equations. Trial and error, or a systematic approach considering the constraints (non-negative integers, max of 12 spools), can lead to the solution.
Here is an example of using trial and error:
- Start with z (the largest value - 8 yards) and try the maximum number of spools with 8 yards that does not exceed 68 when multiplied by 8.
- Calculate the remaining yards and divide them by 5 to see if the quotient plus z spools is less than or equal to 12.
- If not, decrease the number of z spools by one and repeat step 2.
- Once a suitable number for z spools is found, determine the possible values for x and y that satisfy both equations.
By following this process, a solution that fits is found: 4 spools of 3 yards, 5 spools of 5 yards, and 3 spools of 8 yards.
Thus, the number of spools of each length of ribbon that Sabrina has are:
- 3-yard spools: 4
- 5-yard spools: 5
- 8-yard spools: 3