Marco paints a wall and charges $20 as set up fee. He charges at least $60 per big wall and he for small walls he charges no more than $40 per wall.He has just completed painting either all big walls or small walls.
His invoice states that he received $2420 in payment.How many walls could he have painted?
I did like this, 20+60b<=2420
b<= 60 big walls
or 20+40s>=2420
s>=40 small walls.
so , atmost 60 big walls or atleast 40 small walls. Is this correct? Please help me.
at most 40 big walls
(less, if he charges more than $60 each)
at least 60 small walls
(more, if he charges less than $40 each)
Your approach is almost correct. Let's break down the problem and solve it step by step.
Let:
b = number of big walls
s = number of small walls
According to the information given:
1. Marco charges at least $60 per big wall, so the total amount for big walls would be 60b.
2. Marco charges no more than $40 per small wall, so the total amount for small walls would be 40s.
3. Marco charges a set-up fee of $20, which is the same for any number of walls.
So, the total invoice amount can be calculated as: (set-up fee) + (total amount for big walls) + (total amount for small walls)
Invoice Amount = 20 + 60b + 40s
We are given that the total invoice amount received is $2420. So we have the equation:
20 + 60b + 40s = 2420
Now let's analyze the requirements given:
1. Marco has just completed painting either all big walls or only small walls.
This means that he painted either all big walls (b) or all small walls (s). Not a combination.
If he painted only big walls (b), then the total invoice amount would be 60b + 20.
If he painted only small walls (s), then the total invoice amount would be 40s + 20.
Now let's solve the equation and find the possible values for b and s.
1. If Marco painted all big walls:
60b + 20 = 2420
60b = 2400
b = 40
This means Marco painted 40 big walls.
2. If Marco painted all small walls:
40s + 20 = 2420
40s = 2400
s = 60
This means Marco painted 60 small walls.
Therefore, Marco could have painted either 40 big walls or 60 small walls.
Please note that the equation you wrote, 20 + 60b ≤ 2420, is incorrect because it does not account for the set-up fee and assumes that Marco charges exactly $60 for each big wall. Similarly, the equation you wrote for small walls, 20 + 40s ≥ 2420, is also incorrect because it assumes Marco charges exactly $40 for each small wall. Always make sure to consider all the given information in the problem and the conditions mentioned.