A fabric store sells two types of ribbon. One customer buys 3 rolls of the lace ribbon and 2 rolls of the satin ribbon and has a total of 120 yards of ribbon. Another customer buys 2 rolls of the lace ribbon and 4 rolls of the satin ribbon and has a total of 160 yards of ribbon.
How many yards are on one roll of lace ribbon and one roll of satin ribbon?
A.
There are 20 yards on one roll of lace ribbon and there are 30 yards on one roll of satin ribbon.
B.
There are 10 yards on one roll of lace ribbon and there are 40 yards on one roll of satin ribbon.
C.
There are 40 yards on one roll of lace ribbon and there are 10 yards on one roll of satin ribbon.
D.
There are 30 yards on one roll of lace ribbon and there are 20 yards on one roll of satin ribbon
Let's assume that there are x yards on one roll of lace ribbon and y yards on one roll of satin ribbon.
From the information given, the first customer bought 3 rolls of lace ribbon and 2 rolls of satin ribbon, so they have a total of 3x yards of lace ribbon and 2y yards of satin ribbon.
The second customer bought 2 rolls of lace ribbon and 4 rolls of satin ribbon, so they have a total of 2x yards of lace ribbon and 4y yards of satin ribbon.
According to the problem, the first customer has a total of 120 yards of ribbon and the second customer has a total of 160 yards of ribbon.
This can be written as a system of equations:
3x + 2y = 120
2x + 4y = 160
To solve this system of equations, multiply the first equation by 2 and the second equation by -3, then add the resulting equations together:
6x + 4y = 240
-6x - 12y = -480
-8y = -240
Divide both sides by -8:
y = 30
Substitute this value of y = 30 into the first equation to solve for x:
3x + 2(30) = 120
3x + 60 = 120
3x = 60
Divide both sides by 3:
x = 20
Therefore, there are 20 yards on one roll of lace ribbon and 30 yards on one roll of satin ribbon.
Therefore, the answer is A. There are 20 yards on one roll of lace ribbon and 30 yards on one roll of satin ribbon.