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Santa’s workshop produces toy trucks and dolls. Each toy truck costs $4.00 and each doll costs $5.00 to make. In one hour the workshop produced a combined total of 105 toy trucks and dolls, and spent $480 in production costs, how many toy trucks and how many dolls were made in that hour?

Sagot :

sqdancefan

Answer:

  • 45 trucks
  • 60 dolls

Step-by-step explanation:

Let t and d represent the numbers of trucks and dolls produced. The given relations let us write two equations:

  t + d = 105

  4t +5d = 480

Substituting for t, we have ...

  4(105 -d) +5d = 480

  d +420 = 480 . . . . . . . . . simplify

  d = 60 . . . . . . . . . . . . subtract 480

  t = 105 -d = 45

45 trucks and 60 dolls were produced in that hour.

S O L U T I O N:

Let's assume the no. of toy trucks be 't' and the no. of dolls produced 'd'

From the above condition as been expressed in question we can frame two equations i.e,

[tex]:\implies\tt{t + d = 105 \: ...(1)} [/tex]

[tex]:\implies\tt{t = 105 - d}[/tex]

[tex]:\implies\tt{4t + 5d = 480 \: ...(2)}[/tex]

Placing the value of t in equation (2),

[tex]:\implies\tt{4(105 - d) + 5d = 480}[/tex]

[tex]:\implies\tt{420 - 4d + 5d = 480}[/tex]

[tex]:\implies\tt{1d = 480 - 420}[/tex]

[tex]:\implies\tt{d = 60}[/tex]

Placing value of d in eqn (1),

[tex]:\implies\tt{t + d = 105}[/tex]

[tex]:\implies\tt{t + 60 = 105}[/tex]

[tex]:\implies\tt{t = 105 - 60}[/tex]

[tex]:\implies\tt{t = 45}[/tex]

  • Dolls produced were 60 and toy trucks produced were 45.
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