150 children have to go on a school
tour. They can use minibuses, which
carry x pupils each, or cars which
carry y pupils each. The
mathematics teacher works out that
they could just manage with 10 minibuses and 6 cars, or with 5
minibuses and 18 cars. Write down
two equations and hence find the
value of x and y.
pls help me i dont know what to do next
m minibuses
m x number in minis
n cars
n y = number in cars
10 minibuses means m = 10
10 x in buses
6 cars means n = 6
6 y in cars
so
10 x + 6 y = 150
but also
5x + 18 y = 150
now we have a plain old 2 eqn, 2 unknown problem
multiply the second equation by 2 and we have:
10 x + 6 y = 150
10 x + 36y = 300
----------------- subtract
-30 y = -150
so
y = 5
go back and get x now
10x+6(5) = 150
10 x = 120
x = 12
(12, 5)
wow! Thank u somuch Damon. May God bless u
To solve this problem, we can set up a system of equations.
Let's denote:
x = number of pupils each minibus carries
y = number of pupils each car carries
We have the following information given in the problem:
1) 10 minibuses and 6 cars can accommodate the 150 children.
2) 5 minibuses and 18 cars can also accommodate the 150 children.
From these two pieces of information, we can set up the following equations:
Equation 1:
10x + 6y = 150
Equation 2:
5x + 18y = 150
Now, we can solve this system of equations to find the values of x and y.
There are different methods to solve systems of equations, such as substitution or elimination. Let's solve it using the elimination method.
Multiply Equation 1 by 3 and Equation 2 by 2 to make the coefficients of x in both equations equal:
Equation 1 multiplied by 3:
30x + 18y = 450
Equation 2 multiplied by 2:
10x + 36y = 300
Now, we can subtract Equation 2 from Equation 1 to eliminate x:
(30x + 18y) - (10x + 36y) = 450 - 300
Simplifying, we get:
20x - 18y = 150
Now, we have one equation in terms of x and y. Let's call this Equation 3:
Equation 3:
20x - 18y = 150
To solve this equation, we can divide both sides by 2:
10x - 9y = 75
Now, we have two equations:
Equation 10x - 9y = 75
Equation 5x + 18y = 150
From Equation 10x - 9y = 75, we can isolate x:
10x = 9y + 75
x = (9y + 75) / 10
Now, substitute this expression for x in Equation 5x + 18y = 150:
5((9y + 75) / 10) + 18y = 150
Multiply both sides by 10 to get rid of the denominator:
5(9y + 75) + 180y = 1500
45y + 375 + 180y = 1500
225y = 1500 - 375
225y = 1125
y = 1125 / 225
y = 5
Now, substitute the value of y = 5 back into Equation 1 to find x:
10x + 6(5) = 150
10x + 30 = 150
10x = 150 - 30
10x = 120
x = 120 / 10
x = 12
Therefore, the value of x is 12 and the value of y is 5.