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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

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

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

Solução

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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.

Explicação

## Step 1<br />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:<br />### \(a + c = 10\)<br /><br />## Step 2<br />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:<br />### \(185a + 75c + 10 + 5 + 335 = 1595\)<br /><br />## Step 3<br />Simplify the equation from Step 2 to:<br />### \(195a + 80c + 335 = 1595\)<br /><br />## Step 4<br />Subtract 335 from both sides of the equation from Step 3 to isolate the terms with \(a\) and \(c\):<br />### \(195a + 80c = 1260\)<br /><br />## Step 5<br />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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