Question

Farah found 6 rolls of blue ribbon and yellow ribbon. Each roll of blue ribbon was 10 meters long and each roll of yellow ribbon was 9 meters long. If Farah found 58 meters of ribbon in total, how many rolls of each color did she find?

______ Rolls of Blue Ribbon

______ Rolls of Yellow ribbon

Answer 1

Rolls of Blue Ribbon (B)
Rolls of Yellow ribbon (Y)


`\left \{ {{B + Y=6} \atop {10B + 9Y=58}} \right.`

simplify by (-9), equation (I), we have:


`\left \{ {{B + Y=6}.(-9)\atop {10B + 9Y=58}} \right.`


`\left \{ {{-9B -9Y=-54}\atop {10B + 9Y=58}} \right.`


`\left \{ {{-9B -\diagup\!\!\!\!9Y=-54}\atop {10B + \diagup\!\!\!\!9Y=58}} \right.`


`\left \{ {{-9B=-54}\atop {10B=58}} \right.`


`\boxed{B=4}`

Now, we will replace the found value (B) in equation (I), to find the value of (Y), thus:

B + Y = 6
4 + Y = 6
Y = 6 - 4

`\boxed{Y = 2}`

Answer:
Rolls of Blue Ribbon (B) = 4
Rolls of Yellow ribbon (Y) = 2