Solve the problem using matrices.
-Jerry has three pieces of string. The total length is $91 \mathrm {~cm}$. The sum of the two longer pieces is $76 \mathrm {~cm}$. The middle piece is twice as long as the shortest piece. What are the lengths of the three pieces?
A) No solution
B) $15 \mathrm {~cm} ; 30 \mathrm {~cm} ; 46 \mathrm {~cm}$
C) $7.5 \mathrm {~cm} ; 15 \mathrm {~cm} ; 68.5 \mathrm {~cm}$
D) $15 \mathrm {~cm} ; 46 \mathrm {~cm} ; 56 \mathrm {~cm}$

Question

Quizplus · Accepted Answer

The problem can be solved by setting up a system of equations and then using matrices to solve it. Let the lengths of the shortest, middle, and longest pieces be $x$, $2x$, and $y$ respectively. The equations are: $x + 2x + y = 91$, $2x + y = 76$. Solving these gives $x = 15$, $y = 46$, so the lengths are $15 \mathrm {~cm}$, $30 \mathrm {~cm}$, $46 \mathrm {~cm}$.

Solve the Problem Using Matrices 91 cm91 \mathrm {~cm}91 cm the Sum of the Two Longer Pieces Is

Solve the Problem Using Matrices $91 \mathrm {~cm}$ the Sum of the Two Longer Pieces Is