Solve the following word problems / applications involving linear systems
1.Mr. Banks had $260.00 worth of five dollar bills and ten dollar bills. If he had 33 bills in total, how many of each bill did he have?
2 At a dog show in
Calgary, between the number of humans and the number of dogs, there were a total of 36 heads and 102 legs in the ring. How many dogs were in the ring?
1 - Let the number of five-dollar bills =F
Then, the number of ten-dollar bills =33 - F
5F + 10*[33 - F] =260
5F + 330 - 10F =260
- 5F =260 - 330
- 5F = - 70
F = - 70 / - 5
F = 14 - Number of 5-dollar bills
33 - 14 = 19 - Number of 10-dollar bills
Check: [14 x $5 + 19 x $10] =$70 + $190 =$260
2 - Let the number of Human heads = H
Then, the number of dog heads =36 - H
H x 2 legs each + [36 - H] * 4 legs each = 102 legs
2H + 144 - 4H = 102
- 2H = 102 - 144
- 2H = - 42
H =- 42 / -2 =21 - Number of Humans at the Fair.
36 - 21 = 15 - Number of dogs at the Fair.
Check: [21 x 2 legs + 15 x 4 legs] =42 + 60 =102 legs at the Fair.
