Question

User you are task by your employer who purchased 60ft of narra and 80ft of pine wood for a total cost of 31460 pesos. A second purchase of the same prices includes 100ft of narra and 60ft of pine wood for a total cost of 43560 pesos. You are task by your employer to find the cost per foot of nara and pine. Elimination method

Answer 1

The cost per foot of narra wood is 228.56 pesos and the cost per foot of pine wood is 221.83 pesos.

Step-by-step explanation:

To find the cost per foot of narra and pine wood, we can use the elimination method. Let's set up two equations using the given information:

60ft of narra + 80ft of pine = 31460 pesos (Equation 1)

100ft of narra + 60ft of pine = 43560 pesos (Equation 2)

We can solve these equations using the elimination method by multiplying Equation 1 by 100 and Equation 2 by 60:

6000ft of narra + 8000ft of pine = 3146000 pesos (Equation 1)

6000ft of narra + 3600ft of pine = 2613600 pesos (Equation 2)

Now, subtract Equation 2 from Equation 1 to eliminate the narra:

(6000ft of narra + 8000ft of pine) - (6000ft of narra + 3600ft of pine) = 3146000 pesos - 2613600 pesos

2400ft of pine = 532400 pesos

Divide both sides of the equation by 2400 to find the cost per foot of pine:

1ft of pine = 532400 pesos ÷ 2400ft = 221.83 pesos/ft

Therefore, the cost per foot of pine wood is 221.83 pesos.

Substitute the found value of 1ft of pine (221.83 pesos/ft) into Equation 1 to find the cost per foot of narra:

60ft of narra + 80ft of pine = 31460 pesos

60ft of narra + 80ft × 221.83 pesos/ft = 31460 pesos

60ft of narra + 17746.4 pesos = 31460 pesos

Subtract 17746.4 pesos from both sides of the equation:

60ft of narra = 31460 pesos - 17746.4 pesos

60ft of narra = 13713.6 pesos

Divide both sides of the equation by 60 to find the cost per foot of narra:

1ft of narra = 13713.6 pesos ÷ 60ft = 228.56 pesos/ft

Therefore, the cost per foot of narra wood is 228.56 pesos.