24 students and teachers rode to the zoo in vans and 385 students and teachers rode to the zoo in buses.
Step-by-step explanation:
Given,
Total number of students and teachers = 409
Students and teachers in each bus = 55
Students and teachers in each van = 12
Let,
x be the number of buses
y be the number of vans
55x+12y=409 Eqn 1
x = y+5 Eqn 2
Putting value of x from Eqn 2 in Eqn 1
[tex]55(y+5)+12y=409\\55y+275+12y=409\\67y=409-275\\67y=134[/tex]
Dividing both sides by 67
[tex]\frac{67y}{67}=\frac{134}{67}\\y=2[/tex]
Putting y=2 in Eqn 2
[tex]x=2+5\\x=7[/tex]
Number of students and teachers who rode in vans = Number of vans * Teachers and student in each van
Number of students and teachers who rode in vans = 12*2 = 24
Number of students and teachers who rode in buses = 7*55 = 385
24 students and teachers rode to the zoo in vans and 385 students and teachers rode to the zoo in buses.
Keywords: linear equation, substitution method
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Answer:
385 students and teachers rode to the zoo in buses
24 students and teachers rode to the zoo in vans
Step-by-step explanation:
Let b = total number of buses
Let v = total number of vans
Given:
Create 2 equations from the given information:
Equation 1: 55b + 12v = 409
Equation 2: b = 5 + v
Substitute Equation 2 into Equation 1 and solve for v:
⇒ 55(5 + v) + 12v = 409
⇒ 275 + 55v + 12v = 409
⇒ 275 + 67v = 409
⇒ 67v = 134
⇒ v = 2
Substitute the found value of v into Equation 2 and solve for b:
⇒ b = 5 + 2
⇒ b = 7
Therefore, there were:
To find the number of students who road to the zoo in the vans and buses, multiply the given number of students and teachers each vehicle transported by the found number of vehicles used:
⇒ Buses 55 × 7 = 385
⇒ Vans: 12 × 2 = 24
Therefore:
