Question

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?
OA. There are 10 yards on one roll of lace ribbon and there are 40 yards on one roll of satin ribbon.
OB. There are 20 yards on one roll of lace ribbon and there are 30 yards on one roll of satin ribbon.
OC. There are 30 yards on one roll of lace ribbon and there are 20 yards on one roll of satin ribbon.
OD. There are 40 yards on one roll of lace ribbon and there are 10 yards on one roll of satin ribbon.

Answer 1

20 yards in the lace ribbon and there are 30 yards on one roll of satin ribbon

Explanation:

3x + 2y = 120 (1)

2x + 4y = 160 (2)

Divide eq(2) by 2 (both sides). Keep equation (1) as is. You will get

3x + 2y = 120 (1')

x + 2y = 80 (2')

Now subtract eq(2') from eq(1'). You will get

2x = 120 - 80 = 40

x = 40/2 = 20.

Then from equation (2'),

20 + 2y = 80

2y = 80 - 20 = 60

y = 60/2 = 30

Answer 2

B

Explanation:

3(20)=60

2(30)=60

60+60=120

2(20)= 40

4(30)= 120

40+120=160