Question

HELP QUICK PLEASE!!!
A defective scale shows a false weight that always differs from the actual weight by a few ounces (either greater or less). When a box was put on the scale it showed 15 ounces. When a bag was put on the scale it showed 12 ounces. When the box and the bag are put on the scales together, it showed 31 ounces. What is the weight of the box?

Answer 1

Answer:

$b=19\ ounces$

Step-by-step explanation:

System Of Equations

We know the scale shows a false reading for the weights by a constant value. Let's call e the weight it adds or subtracts from the real weight it measures.  

When the box is put on the scale, the real weight is b, but the scale shows

$b+e=15$

When the bag is weighted, the real value is g, but the scale shows

$g+e=12$

Finally, when both are measures, the real weight is b+g and the scale shows

$b+g+e=31$

We have formed a system of equations. It's easy to find the value of b, we just need to subtract the last two equations

$b+g+e-g-e=31-12$

$\boxed{b=19\ ounces}$