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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?

Jul 23, 2020

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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.

Jul 23, 2020