Math Problem Knot

Question

You are assigned by High School to design a playground as part of your volunteer service. The playground consists of two brands of rope used for ladder assembly. Brand XX of rope takes 44 hours to knot and 22 hours to assemble as a ladder. Brand YY of rope takes 66 hours to knot and 1010 hours to assemble as a ladder. If you are given exactly 120120 hours for knotting and exactly 130130 hours for assembly, complete the following questions to determine how many ladders of each type of rope will be ready for playground assembly using all the available time. 

Create a system of equations for the situation using x for Brand X of rope and y for Brand Y of rope.

Equation 1:   

Equation 2:   

Answer 1

Let x = no. ladders with Brand X rope; y = no. ladders with Brand Y rope.

Brand X ladders need 4 hrs to knot, 2 hrs assy.

Brand Y need 6 hrs to knot, 10hrs assy. Given that total knot hours = 120; total assy hrs = 130.

For the knots: 4x + 6y = 120

For assy: 2x + 10y = 130 Can elim x terms by multiplying 2nd eqn by -2.

4x + 6y = 120

-4x - 20y = -260

-14y = -140 y = 10 ladders

You can calculate the no. of x ladders by substituting y = 10 into either of the original eqns and solving for x.