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 40 yards on one roll of lace ribbon and there are 10 yards on one roll of satin ribbon.
B.
There are 20 yards on one roll of lace ribbon and there are 30 yards on one roll of satin ribbon.
C.
There are 30 yards on one roll of lace ribbon and there are 20 yards on one roll of satin ribbon.
D.
There are 10 yards on one roll of lace ribbon and there are 40 yards on one roll of satin ribbon.
Answers
Given : 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.
To Find :
How many yards are on one roll of lace ribbon and one roll of satin ribbon?
A. There are 40 yards on one roll of lace ribbon and there are 10 yards on one roll of satin ribbon.
B. There are 20 yards on one roll of lace ribbon and there are 30 yards on one roll of satin ribbon.
C. There are 30 yards on one roll of lace ribbon and there are 20 yards on one roll of satin ribbon.
D. There are 10 yards on one roll of lace ribbon and there are 40 yards on one roll of satin ribbon.
Solution:
one roll of lace ribbon = x yard
one roll of satin ribbon = y yard
One customer buys 3 rolls of the lace ribbon and 2 rolls of the satin ribbon and has a total of 120 yards
=> 3x + 2y = 120
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.
=> 2x + 4y = 160
=> x + 2y = 80
3x + 2y = 120
x + 2y = 80
=> 2x = 40
=> x = 20
=> y = 30
There are 20 yards on one roll of lace ribbon and there are 30 yards on one roll of satin ribbon.
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