4x As a safety feature for a hotel's elevator system, the total weight of the passengers and luggage in an elevator is displayed on a screen in each elevator. Additionally, a buzzer sounds and the doors will not close if the total weight excoeds the maximum 1,600 pound limit. A group of 10 individuals. a combination of adults and children, traveling together squeezes onto an elevator. One person presses their floor number. They all breathe a sigh of relief when the doors close and the elevator starts moving. The total weight displayed on the screen is 1,595 pounds Whew! That was close! - Assume on average that an adult weighs 185 pounds and that each adult has an additional 10 pounds of personal items. - Assume on average that a child weighs 75 pounds and that each child has an additional 5 pounds of personal items. - The total weight of the group's luggage, in addition to their personal items, is 335 pounds - If a represents the number of adults on the elevator and c represents the number of children on the elevator.which two equations represent the constraints of this scenario? - How many adults and how many children were on the elevator in this scenario? a+c=10 185a+75c+10+5+335=1595 195a+80c=1595 195a+80c+335=1595 x There are 7 adults on the elevator. 4x There are 6 adults on the elevator 4x There are 5 adults on the elevator. 4x There are 4 adults on the elevator 4x There are 3 adults on the elevator. There are 7 children on the elevator. D There are 6 children on the elevator. 4x There are 5 children on the elevator x There are 4 children on the elevator. 4x There are 3 children on the elevator. 190a+85c+335=1595

Question

Pergunta

4x As a safety feature for a hotel's elevator system, the total weight of the passengers and luggage in an elevator is displayed on a screen in each elevator. Additionally, a buzzer sounds and the doors will not close if the total weight excoeds the maximum 1,600 pound limit. A group of 10 individuals. a combination of adults and children, traveling together squeezes onto an elevator. One person presses their floor number. They all breathe a sigh of relief when the doors close and the elevator starts moving. The total weight displayed on the screen is 1,595 pounds Whew! That was close! - Assume on average that an adult weighs 185 pounds and that each adult has an additional 10 pounds of personal items. - Assume on average that a child weighs 75 pounds and that each child has an additional 5 pounds of personal items. - The total weight of the group's luggage, in addition to their personal items, is 335 pounds - If a represents the number of adults on the elevator and c represents the number of children on the elevator.which two equations represent the constraints of this scenario? - How many adults and how many children were on the elevator in this scenario? a+c=10 185a+75c+10+5+335=1595 195a+80c=1595 195a+80c+335=1595 x There are 7 adults on the elevator. 4x There are 6 adults on the elevator 4x There are 5 adults on the elevator. 4x There are 4 adults on the elevator 4x There are 3 adults on the elevator. There are 7 children on the elevator. D There are 6 children on the elevator. 4x There are 5 children on the elevator x There are 4 children on the elevator. 4x There are 3 children on the elevator. 190a+85c+335=1595

Answer 1

The correct equations are

$a + c = 10$ and

$195a + 80c = 1260$ . The correct number of adults and children on the elevator is 6 adults and 4 children.

Answer 2

## Step 1
The problem involves two unknowns,

$a$ and

$c$ , which represent the number of adults and children respectively. The total number of people in the elevator is 10, which gives us the first equation:
###

$a + c = 10$

## Step 2
The total weight of the people and their personal items is 1595 pounds. Given that an adult weighs 185 pounds and carries an additional 10 pounds of personal items, and a child weighs 75 pounds and carries an additional 5 pounds of personal items, we can express the total weight as:
###

$185a + 75c + 10 + 5 + 335 = 1595$

## Step 3
Simplify the equation from Step 2 to:
###

$195a + 80c + 335 = 1595$

## Step 4
Subtract 335 from both sides of the equation from Step 3 to isolate the terms with

$a$ and

$c$ :
###

$195a + 80c = 1260$

## Step 5
Now we have two equations,

$a + c = 10$ and

$195a + 80c = 1260$ . We can solve this system of equations to find the values of

$a$ and

$c$ .

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