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A motel clerk counts his $10 bills and $20 bills at the end of the day. He finds that he has a total of 150 bills, and that those 150 bills have a total value of $2,000. How many $10 bills and $20 bills does the motel clerk have?

Translate the problem into 2 equations.


Let the x be the number of $10 bills and y be the number of $20 bills.

Respuesta :

MrRoyal

Answer:

100 $10 bills and

50 $20 bills

Step-by-step explanation:

Given

[tex]x = \$10[/tex]

[tex]y = \$20[/tex]

[tex]Bills = 150[/tex]

[tex]Value = \$2000[/tex]

Required

Determine the number of $10 and $20 bills

[tex]Bills = 150[/tex].

This implies that:

[tex]x + y = 150[/tex]

[tex]Value = \$2000[/tex]

This implies that:

[tex]10x + 20y = 2000[/tex]

So, the equations are:

[tex]x + y = 150[/tex]

[tex]10x + 20y = 2000[/tex]

Make x the subject in the first equation

[tex]x = 150 -y[/tex]

Substitute 150 - y for x in the second

[tex]10(150 - y) + 20y= 2000[/tex]

[tex]1500 - 10y + 20y= 2000[/tex]

[tex]1500 + 10y = 2000[/tex]

[tex]10y = 2000-1500[/tex]

[tex]10y = 500[/tex]

[tex]y =50[/tex]

Recall that:

[tex]x = 150 -y[/tex]

[tex]x = 150 -50[/tex]

[tex]x = 100[/tex]

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