Question

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?

Answer 1

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,

`:\implies\tt{t + d = 105 \: ...(1)}`

`:\implies\tt{t = 105 - d}`

`:\implies\tt{4t + 5d = 480 \: ...(2)}`

Placing the value of t in equation (2),

`:\implies\tt{4(105 - d) + 5d = 480}`

`:\implies\tt{420 - 4d + 5d = 480}`

`:\implies\tt{1d = 480 - 420}`

`:\implies\tt{d = 60}`

Placing value of d in eqn (1),

`:\implies\tt{t + d = 105}`

`:\implies\tt{t + 60 = 105}`

`:\implies\tt{t = 105 - 60}`

`:\implies\tt{t = 45}`

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

Answer 2

• 45 trucks
• 60 dolls

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.