Question

1. mathematical connections the sum of 5 times the width of a rectangle and twice its length is 26 units. the difference of 15 times the width and three times the length is 6 units. write and solve a system of equations to find the length and width of the rectangle.

Explanation:

Step1: Set up the equations

Let \( w \) be the width and \( l \) be the length.
First equation: \( 5w + 2l=26 \)
Second equation: \( 15w-3l = 6 \)

Step2: Multiply the first equation

Multiply \( 5w + 2l=26 \) by \( 3 \) to get \( 15w+6l = 78 \)

Step3: Subtract the second equation from the new first equation

\((15w + 6l)-(15w-3l)=78 - 6\)
\(15w+6l - 15w + 3l=72\)
\(9l=72\)
\(l = 8\)

Step4: Substitute \( l = 8 \) into the first original equation

\(5w+2\times8=26\)
\(5w+16 = 26\)
\(5w=26 - 16\)
\(5w=10\)
\(w = 2\)

Answer:

The length of the rectangle is \( 8 \) units and the width is \( 2 \) units.