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A bank teller has 47 $20 and $5 bills in her cash drawer. The value of the bills is $490. How many $20 bills are
there?

Respuesta :

Answer:

A bank teller has 47 $20 and $5 bills.

The value of the bills is $490.

Number of $20 bills --> x

Number of $5 bills --> y

x + y = 47 --> x = 47-y

20x + 5y = 490 --> 20x = 490-5y

so

20(47-y) = 490 -5y

940-20y = 490-5y

940-490 = -5y+20y

15y = 450

y= 30

so

x = 47-30

x = 17

IN TOTAL --> 17 $20 bills and 30 $5 bills.

Space

Answer:

x = 17 $20 bills

y = 30 $5 bills

General Formulas and Concepts:

  • Order of Operations: BPEMDAS
  • Multivariable Systems

Step-by-step explanation:

Step 1: Define variables

x = # of $20 bills

y = # of $5 bills

Step 2: Set up systems of equations

[tex]\left \{ {{x+y=47} \atop {20x+5y=490}} \right.[/tex]

Step 3: Solve for x

  1. Rewrite:                                        [tex]\left \{ {{y=47-x} \atop {20x+5y=490}} \right.[/tex]
  2. Substitute:                                     [tex]20x+5(47-x)=490[/tex]
  3. Distribute 5:                                   [tex]20x+235-5x=490[/tex]
  4. Combine like terms:                     [tex]15x+235=490[/tex]
  5. Subtract 235 on both sides:        [tex]15x=255[/tex]
  6. Divide both sides by 15:               [tex]x=17[/tex]

By solving for x, we now know that we have 17 $20 bills.

Step 4: Solve for y

  1. Define:                                        x + y = 47
  2. Substitute:                                  17 + y = 47
  3. Subtract 17 on both sides:         y = 30

Now we know that we have 30 $5 bills.

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