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How Do You Solve a Word Problem by Writing an Equation and Plugging in Values?

Amit and Betty work at the algebra Inn, a restaurant known for its complicated contracts. Amit's contract says he gets paid a dollar amount equal to twice the sum of Amit's hours and two times Betty's hours plus one half of Betty's hours squared plus two times the sum of Amit's hours and three times Betty's hours. If Amit worked 30 hours and Betty worked 10 hours how much much does Amit get paid?

Summary

  1. The variable 'm' is equal to the amount of money that Amit makes
  2. 'a' is equal to the number of hours Amit worked
  3. 'b' is equal to how many hours Betty worked
  4. Distribute the twos inside their parentheses
  5. Combine '2a' and '2a' together to get '4a'
  6. Combine '4b' and '6b' together to get '10b'
  7. Just bring down 'one half b2'
  8. Amit is paid $270!!

Notes

    1. The variable 'm' is equal to the amount of money that Amit makes
    1. The variable 'a' is equal to the number of hours Amit worked
    2. The variable 'b' is equal to the number of hours Betty worked
    1. Amit gets paid a dollar amount equal to, m=
    2. Twice the sum of Amit's hours and two times Betty's hours, 2(a+2b)
    3. Plus one half of Betty's hours squared, +(1/2)•b2
    4. Plus two times the sum of Amit's hours and three times Betty's hours, +2(a+3b)
    1. We still have 'm' on the left hand side
    2. Distribute the '2' inside the parentheses to get '2a+4b'
    3. Then add our 'one half b2'
    4. Then distribute the second '2' to get '2a+6b'
    1. Like terms are color coded and have the same color
    1. The variable 'a' is equal to the number of hours Amit worked
    2. The variable 'b' is equal to the number of hours Betty worked
    1. The variable 'b' is equal to the number of hours Betty worked
    1. The variable 'a' is equal to the number of hours Amit worked
    2. The variable 'b' is equal to the number of hours Betty worked
    1. 'a' stands for how many hours Amit worked, so 'a' is thirty hours
    2. 'b' stands for how many hours Betty worked, so 'b' is ten hours
    1. The variable 'm' is equal to the amount of money that Amit makes
    2. 'm' is still on the left hand side
    3. We plug 30 in for 'a' here
    4. We plug 10 in for 'b' here
    5. And we plug 10 in for 'b' here, as well
    1. The variable 'm' is equal to the amount of money that Amit makes
    2. First complete the square, 102=10•10=100
    3. Then perform the multiplication, half of 100 is 50
    4. Lastly, add everything together to get 270!