Examkin

Soru

Zorluk: KolaySimultaneous Equations and Systems

A logistics company packages cargo into two types of containers: Standard containers and Heavy-duty containers.

A shipment of 33 Standard containers and 22 Heavy-duty containers has a total mass of 1,4001,400 kilograms. A second shipment of 22 Standard containers and 44 Heavy-duty containers has a total mass of 2,0002,000 kilograms.

Based on this information, select the value in kilograms for the mass of a single Standard container and for the mass of a single Heavy-duty container so that the selections are consistent with the given information.

  • Mass of a single Standard container (kg)200
  • Mass of a single Heavy-duty container (kg)400

Cevap

The mass of a single Standard container is 200 kg, and the mass of a single Heavy-duty container is 400 kg.
Setting up the simultaneous linear equations 3s+2h=14003s + 2h = 1400 and 2s+4h=20002s + 4h = 2000 yields s=200s = 200 and h=400h = 400. Thus, selecting 200 for the Standard container column and 400 for the Heavy-duty container column correctly matches the calculated values.

Adım Adım Çözüm

1
Define variables and set up the system of equations from the problem stem.
Let ss be the mass of a Standard container in kg and hh be the mass of a Heavy-duty container in kg. The given shipments yield:
Equation 1: 3s+2h=14003s + 2h = 1400
Equation 2: 2s+4h=20002s + 4h = 2000
Translate word problem conditions into algebraic equations.
2
Simplify Equation 2 by dividing all terms by 2.
s+2h=1000  ⟹  s=1000−2hs + 2h = 1000 \implies s = 1000 - 2h
Isolate variable ss to use the substitution method.
3
Substitute s=1000−2hs = 1000 - 2h into Equation 1 and solve for hh.
3(1000−2h)+2h=1400  ⟹  3000−6h+2h=1400  ⟹  3000−4h=1400  ⟹  4h=1600  ⟹  h=4003(1000 - 2h) + 2h = 1400 \implies 3000 - 6h + 2h = 1400 \implies 3000 - 4h = 1400 \implies 4h = 1600 \implies h = 400
Determine the value for the mass of a Heavy-duty container.
4
Substitute h=400h = 400 back into s=1000−2hs = 1000 - 2h to solve for ss.
s=1000−2(400)=1000−800=200s = 1000 - 2(400) = 1000 - 800 = 200
Determine the value for the mass of a Standard container.

Anahtar Kavram

Solving two-variable linear systems using substitution or elimination in a Two-Part Analysis format
Bu soruyu puanla

Konular

Simultaneous Equations and Systems

Bu konudan daha fazla soru