Question

Mikaila is saving money to purchase a laptop computer. She already hassaved $150 in her savings account. Next week Mikaila will begin a tutoringjob that pays $10 per hour. All the money she earns tutoring will be added toher savings account.A. What is the total amount of money Mikaila will have saved in her accountafter tutoring for 12 hours? Show or explain how you got your answer.B. Write an expression to represent the total amount of money Mikaila willhave saved in her account after tutoring for x hours.C. The least expensive laptop that Mikaila is considering purchasing costs$550, including tax.Write and solve an inequality to determine the minimum number of hoursMikaila needs to tutor to have enough money in her savings account topurchase a laptop that costs $550 or more. Show or explain how you gotyour answer.D. The most expensive laptop that Mikaila is considering purchasing costs$1,150, including tax.Write and solve a compound inequality to determine the number of hoursMikaila needs to tutor to have enough money in her savings account topurchase a laptop that costs at least $550 but not more than $1,150.Show or explain how you got your answer.

Answer 1

Given:

Amount of money previously saved = $ 150.

Amount of money saved from tutoring job per hour = $ 10.

Required:

( a ) Total amount of money saved after tutoring for 12 hours.

( b ) expression to represent the total amount of money Mikaila saved after working for x hours.

( c ) Inequality to determine the minimum number of hours.

( d ) Compound inequality to determine the number of hours Mikaila needs to tutor to have enough money in her savings account to purchase a laptop that costs at least $550 but not more than $1,1550.

Step-by-step explanation:

( a ) Amount of money saved after tutoring for 12 hours is calculated as,

`Money\text{ saved due to tutoring = 12 }*\text{ 10 = \$ 120}`

Total amount of money saved = $ 150 + $ 120 = $ 270

Thus the total amount of money saved after tutoring for 12 hours is $ 270.

( b ) The amount of money saved after tutoring for x hours is calculated as,

`After\text{ x hours of tutoring = 10x}`

Total amount of money saved after x hours = 10x + $ 150.

Thus the total amount of money saved after tutoring for x hours is 10x + $ 150.

( c ) The required inequality is calculated as,

`Inequality\text{ = 10x + 150 }\ge\text{ 550}`

Inequality representing the minimum number of hours required to purchase a laptop for $ 150 or more is calculated as,

`\begin{gathered} 10x\text{ + 150 }\ge\text{ 550 } \\ 10x\text{ + 150 - 150 }\ge\text{ 550 - 150} \\ 10x\text{ }\ge\text{ 400} \\ x\text{ }\ge\text{ 40} \end{gathered}`

( d ) In inequality represents the number of hours Mikaila needs to work to purchase a laptop that costs more than or equal to $ 150 and less than or equal to $ 1150 is calculated as,

`\begin{gathered} 1150\ge10x\text{ + 150}\ge550 \\ \end{gathered}`

On solving,

`\begin{gathered} 1150\text{ }\ge\text{ 10x + 150} \\ 1150\text{ - 150 }\ge\text{ 10x + 150 - 150} \\ 1000\text{ }\ge\text{ 10x } \\ 100\ge x \\ x\text{ }\leq\text{ 100} \end{gathered}`

Further,

`\begin{gathered} 10x\text{ + 150 }\ge\text{ 550} \\ 10x\text{ + 150 - 150 }\ge\text{ 550 - 150} \\ 10x\text{ }\ge\text{ 400} \\ x\text{ }\ge\text{ 40} \end{gathered}`

Thus the required inequality representing the number of hours is

`40\leq x\leq100`

Answer:

(a) Total amount of money saved after tutoring for 12 hours is $ 270.

(b) Expression to represent the total amount of money Mikaila saved after working for x hours is 10x + $ 150.

(c) Inequality to determine the minimum number of hours for purchasing the laptop for $ 550 or more.

`x\ge40`

(d) Compound inequality to determine the number of hours Mikaila needs to tutor to have enough money in her savings account to purchase a laptop that costs at least $550 but not more than $1,1550 is,

`40\leq x\leq100`