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Problem of the Week
Problem A
Balancing Act

Bailey is in charge of sending out boxes from a distribution centre. The contents of the boxes are identified by shapes stamped on them: a heart, a moon, or a sun. All boxes with the same stamp have the same mass, and the cost of sending a box depends on its mass. Bailey has a balance scale and a few standard weights to help with the job. The following diagrams show what Bailey observed when arranging some of the boxes and standard weights on the scales.

A balanced scale has a box with a heart stamp on the left side and a 2 kilogram weight on the right side.

A balanced scale has a box with a moon stamp along with a box with a sun stamp on the left side, and a 24 kilogram weight on the right side.

A balanced scale has a box with a moon stamp along with a box with a sun stamp on the left side, and two boxes with a heart stamp along with one box with a moon stamp on the right side.

Find the mass of each box.

Themes: Algebra, Number Sense