A linear system fits a jar with two kinds of beads and two facts: the starting total and the total removed. Name the original counts, write one equation for each fact, then graph both in Desmos and click their intersection. Take each removal percent of its own color group. The overall decrease is a percent of the entire jar.
Hints
- Hint 1
A system is two equations about the same unknowns. Let count the original red beads and count the original blue beads. Since every bead was one of those colors, what equation records the starting total?
- Hint 2
A percent decrease uses the amount you started with as its base. Find of the whole jar of beads. That gives the number removed across both colors, not the original number of red beads.
- Hint 3
Each color has its own percent base: acts on the original red count, while acts on the original blue count. Add the amounts removed, then find where that equation meets the starting-total equation.
Step-by-step
Graph the bead-count system
Step 1Write the starting-total equation
Let count the original red beads and count the original blue beads. Every starting bead is one color or the other, so the total gives:
- Step 2
Find the total number removed
The percent decrease applies to the whole starting jar. Type in Desmos. It prints , so beads were removed altogether.
- Step 3
Write the removed-beads equation
The base of each color's percent is that color's original count. So of the red beads removes , and of the blue beads removes . Add those two amounts to match the beads removed:
- Step 4
Read the red count at the intersection
Type and on separate Desmos lines. Click their intersection, the point that makes both equations true. Desmos shows . The first coordinate is , so the jar originally had red beads. Choice B.