Question

three friends play a game. jamila has 4\frac{1}{2} more points than carter. carter has 7\frac{1}{2} more points than aisha. jamila has 26 points. write and solve an equation to find the number of points aisha has. show your work.

Explanation:

Step1: Define variables

Let \( A \) be Aisha's points, \( C \) be Carter's points, and \( J \) be Jamila's points.

Step2: Translate relationships to equations

Jamila has \( 4\frac{1}{2} \) more points than Carter: \( J = C + 4\frac{1}{2} \)
Carter has \( 7\frac{1}{2} \) more points than Aisha: \( C = A + 7\frac{1}{2} \)
Jamila has 26 points: \( J = 26 \)

Step3: Substitute \( J = 26 \) into first equation

\( 26 = C + 4\frac{1}{2} \)
Solve for \( C \): \( C = 26 - 4\frac{1}{2} = 21\frac{1}{2} \)

Step4: Substitute \( C = 21\frac{1}{2} \) into second equation

\( 21\frac{1}{2} = A + 7\frac{1}{2} \)
Solve for \( A \): \( A = 21\frac{1}{2} - 7\frac{1}{2} = 14 \)

Answer:

Aisha has 14 points.