30 children are going on a trip. It costs £5 including lunch. Some children take their own packed lunch. They pay only £3. The 30 children pay a total of £110
How many children are taking their own packed lunch?
number of lunchers ---- x
number of non-lunchers --- 30-x
5x + 3(30-x) = 110
5x + 90 - 3x = 110
2x = 20
x = 10
10 took their own lunch, 20 bought their lunch
check:
10(5) + 20(3) = 110
x = included, y = bring own
y = 30 - x
5x + 3y = 110
Substitute 30-x for y in second equation and solve for x. Insert that value into the first equation and solve for y. Check by inserting both values into the second equation.
Let's assume the number of children who are taking their own packed lunch is x.
So, the number of children who are paying £5 (including lunch) would be 30 - x.
The cost for x children who bring their own lunch would be £3 each, so the total cost for them would be 3x.
The cost for (30 - x) children who have lunch provided would be £5 each, so the total cost for them would be 5(30 - x).
The total cost paid by all 30 children is £110, so we can write the equation as:
3x + 5(30 - x) = 110
Simplifying the equation:
3x + 150 - 5x = 110
-2x = -40
Dividing both sides by -2:
x = -40 / -2
x = 20
So, 20 children are taking their own packed lunch.
To find out how many children are taking their own packed lunch, we need to set up an equation based on the given information. Let's suppose the number of children taking their own packed lunch is x.
The number of children paying the full price, including lunch, is given as 30 - x. They pay £5 each.
The number of children paying only £3 is x.
We know that the total amount paid by the 30 children is £110. So, we can set up the equation:
(30 - x) * £5 + x * £3 = £110
Now, we can solve this equation to find the value of x. Let's simplify the equation:
150 - 5x + 3x = £110
Combine like terms:
-2x + 150 = £110
Subtract £150 from both sides:
-2x = -£40
Divide both sides by -2:
x = £40 / -2
x = 20
So, 20 children are taking their own packed lunch.