Chapter 6.3, Problem 28PPE

To determine

To Explain: Why the worker must have made the mistake.

Answer to Problem 28PPE

As x comes in negative, it cannot be possible, as weight cannot be negative.

Explanation of Solution

Given information: A toy store worker packed two boxes of identical dolls and plush toys for shipping in boxes that weigh 1 OZ, when empty. One box held 3 dolls and 4 plush toys. The worker marked the weight as 12 OZ, the other box held 2 dolls and 3 plush toys. The worker marked the weight as 10 OZ.

Formula used: Solving the linear equationCalculation: Let one doll weigh x and one plush toys weigh y

So $3x+4y+1=12$

Or $3x+4y=11$ ---------------- (1)

  $2x+3y+1=10$

Or $2x+3y=9$ ----------------- (2)

Multiplying equation (1) by 2 and equation (2) by 3 we get

  $6x+8y=22$ ………………………. (3)

  $6x+9y=27$ ……………………… (4)

Subtracting equation (4) by equation (3)

We get $-y=-5$

Or $y=5$

Now substituting the value of y in equation (3)

we have $6x+40=22$

  $6x=-18$

  $x=-3$

Because x is negative, So it is wrong