Question

Which scenario can be represented using the inequalities below? 1.25 < x < 1.5 a container of milk costs at least $1.25 but less than $1.50. a student spends at least 1 hour 15 minutes, but no more than 1 hour 30 minutes on homework. a tip added to a restaurant bill is less than or equal to 25% or less than or equal to 50%. the point value of a test item is more than 1.25 points and less than 1.5 points.

Answer 1

we have

$1.25 < x < 1.5$

Scenarios

case a) A container of milk costs at least $1.25 but less than $1.50

Let

x-------> container of milk costs

we know that

$x\geq 1.25\\ x < 1.50\\ 1.25\leq x < 1.50$

this scenario can not be represented with the inequality of the problem

case b) A student spends at least 1 hour 15 minutes, but no more than 1 hour 30 minutes on homework

Let

x-------> time spend in homework in hours

we know that

$1$ hour $15$ minutes is equal to $1.25$ hours

$1$ hour $30$ minutes is equal to $1.50$ hours

so

$x\geq 1.25\\ x < 1.50\\ 1.25\leq x < 1.50$

this scenario can not be represented with the inequality of the problem

case c) A tip added to a restaurant bill is less than or equal to 25% or less than or equal to 50%

we know that

increase a number $25$% is equal to multiply the number by$1.25$

increase a number $50$% is equal to multiply the number by $1.50$

Let

x-------> a tip added to a restaurant bill

$x\leq 1.25\\ or\\ x\leq 1.50\\ \\ x \leq 1.50$

this scenario can not be represented with the inequality of the problem

case d) The point value of a test item is more than 1.25 points and less than 1.5 points.

Let

x---------> the point value of a test

we know that

$x > 1.25\\ x < 1.50\\ 1.25 < x < 1.50$

this scenario can be represented with the inequality of the problem

therefore

the answer is

The scenario that can be represented with the inequality of the problem is the option

The point value of a test item is more than 1.25 points and less than 1.5 points.

Answer 2

Among the choices, the most likely scenario to be represented by the inequality 1.25 < x < 1.5 would be " a container of milk costs at least $1.25 but less than $1.50 ". This could be applied to when a person on a budget would be shopping for milk. The person could spend at least $1.25 if the chat would be the price of the cheapest brand of milk, but should not spend more than $1.50 on more expensive brands, as the person is on a budget.