Toby has only a balance scale, a single 40 g mass, and a stack of both white and red blocks. (Assume that all white blocks have the same mass and all red blocks have the same mass.) Toby discovers that four white blocks and one red block balance two white blocks, two red blocks, and the 40 g mass. He also finds that five white blocks and two red blocks balance one white block and five red blocks.
a. List the unknown quantities and assign a variable to each.
b. Translate Toby's discoveries into equations.
c. Solve the equations to find a value for each variable.