MATH SOLVE

2 months ago

Q:
# 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? There are 20 yards on one roll of lace ribbon and there are 30 yards on one roll of satin ribbon. There are 30 yards on one roll of lace ribbon and there are 20 yards on one roll of satin ribbon. There are 40 yards on one roll of lace ribbon and there are 10 yards on one roll of satin ribbon. There are 10 yards on one roll of lace ribbon and there are 40 yards on one roll of satin ribbon.

Accepted Solution

A:

Let L be the number of yards on a roll of lace ribbon.
Let S be the number of yards on a roll of satin ribbon.
We can set up two equations.
equation 1: 3L + 2S = 120 yards
equation 2: 2L + 4S = 160 yards
We can multiply (equation 1) by 2 and subtract (equation 2).
equation 1: 6L + 4S = 240 yards
equation 2: 2L + 4S = 160 yards
4L = 80 yards
L = 20 yards
equation 1: 3L + 2S = 120 yards
3(20 yards) + 2S = 120 yards
2S = 60 yards
S = 30 yards
There are 20 yards on a roll of lace ribbon.
There are 30 yards on a roll of satin ribbon.