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?

Question

Mathematics

Claudia Barron

12 January, 00:33

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?

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Zack Simmons · Answer 1

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.