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

Question

9 days ago

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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?

Mathematics

1 answer:

tester [8.8K] · Answer 1 · 2026-03-19T00:40:54+03:00

Let L represent the yards in a roll of lace ribbon and S represent the yards in a roll of satin ribbon. We can formulate two equations: 3L + 2S = 120 yards (Equation 1) and 2L + 4S = 160 yards (Equation 2). If we multiply Equation 1 by 2 and subtract Equation 2, we have: 6L + 4S = 240 yards (Equation 1) and 2L + 4S = 160 yards (Equation 2). Thus, 4L equals 80 yards, leading to L equating to 20 yards. For Equation 1, substituting gives 3(20 yards) + 2S = 120 yards, leading to 2S equal to 60 yards, so S equals 30 yards. Therefore, a roll of lace ribbon contains 20 yards, while a roll of satin ribbon has 30 yards.