Linear raise total earnings Practice Questions (Grade 9)

Warm-upmedium

Jordan earns $\text{\char36}32{,}500$ in her first year as a nurse. She gets the same dollar raise every year and earns $\text{\char36}36{,}400$ in her third year. What is the total of Jordan's earnings during her three years on the job?

Subtract the third-year salary from the first: $\text{\char36}36{,}400 - \text{\char36}32{,}500 = \text{\char36}3{,}900$ . Over three years there are two equal raises, so divide by $3 - 1 = 2$ to get $x = \text{\char36}1{,}950$ . Add $\text{\char36}1{,}950$ each year after the first: $\text{\char36}32{,}500$ , $\text{\char36}34{,}450$ , $\text{\char36}36{,}400$ . Sum all three years: $\text{\char36}103{,}350$ .

Mid-gamemedium

Priya earns $\text{\char36}41{,}500$ in her first year as a librarian. She receives the same dollar raise each year and earns $\text{\char36}47{,}800$ in her fourth year. What is the total of Priya's earnings over her four years at the library?

Subtract the fourth-year salary from the first: $\text{\char36}47{,}800 - \text{\char36}41{,}500 = \text{\char36}6{,}300$ . Over four years there are three equal raises, so divide by $4 - 1 = 3$ to get $x = \text{\char36}2{,}100$ . Add $\text{\char36}2{,}100$ each year after the first: $\text{\char36}41{,}500$ , $\text{\char36}43{,}600$ , $\text{\char36}45{,}700$ , $\text{\char36}47{,}800$ . Sum all four years: $\text{\char36}178{,}600$ .

Mid-gamemedium

Devin is paid $\text{\char36}22$ per hour in his first year at a clinic and works $2{,}000$ hours that year. He receives the same dollar-per-hour raise each year and is paid $\text{\char36}26$ per hour in his fifth year, still working $2{,}000$ hours annually. What is the total of Devin's earnings over his five years?

Devin works $2{,}000$ hours each year, so Year 1 earnings are $\text{\char36}44{,}000$ and Year 5 earnings are $\text{\char36}52{,}000$ . Subtract: $\text{\char36}52{,}000 - \text{\char36}44{,}000 = \text{\char36}8{,}000$ . Over five years there are four equal annual increases, so divide by $5 - 1 = 4$ to get $x = \text{\char36}2{,}000$ . Add $\text{\char36}2{,}000$ each year after the first: $\text{\char36}44{,}000$ , $\text{\char36}46{,}000$ , $\text{\char36}48{,}000$ , $\text{\char36}50{,}000$ , $\text{\char36}52{,}000$ . Sum all five years: $\text{\char36}240{,}000$ .

Mid-gamemedium

Aisha receives a $\text{\char36}27{,}500$ research fellowship in her first year with the same dollar bump each year. Her fellowship is $\text{\char36}32{,}600$ in her fourth year. What is the total fellowship amount Aisha received over those four years?

Subtract the fourth-year fellowship from the first: $\text{\char36}32{,}600 - \text{\char36}27{,}500 = \text{\char36}5{,}100$ . Over four years there are three equal bumps, so divide by $4 - 1 = 3$ to get $x = \text{\char36}1{,}700$ . Add $\text{\char36}1{,}700$ each year after the first: $\text{\char36}27{,}500$ , $\text{\char36}29{,}200$ , $\text{\char36}30{,}900$ , $\text{\char36}32{,}600$ . Sum all four years: $\text{\char36}120{,}200$ .

Mid-gamemedium

Carlos earns $\text{\char36}52{,}000$ in his first year as a store manager. He gets the same dollar raise every year and earns $\text{\char36}60{,}800$ in his fifth year. What is the total of Carlos's earnings during his five years at the store?

Subtract the fifth-year salary from the first: $\text{\char36}60{,}800 - \text{\char36}52{,}000 = \text{\char36}8{,}800$ . Over five years there are four equal raises, so divide by $5 - 1 = 4$ to get $x = \text{\char36}2{,}200$ . Add $\text{\char36}2{,}200$ each year after the first: $\text{\char36}52{,}000$ , $\text{\char36}54{,}200$ , $\text{\char36}56{,}400$ , $\text{\char36}58{,}600$ , $\text{\char36}60{,}800$ . Sum all five years: $\text{\char36}282{,}000$ .

Mid-gamemedium

Mei's sales position pays a $\text{\char36}31{,}000$ base in her first year plus the same fixed annual increase to that base each year. Her base is $\text{\char36}35{,}200$ in her third year. What is the total of Mei's base pay over her three years?

Subtract the third-year base from the first: $\text{\char36}35{,}200 - \text{\char36}31{,}000 = \text{\char36}4{,}200$ . Over three years there are two equal increases, so divide by $3 - 1 = 2$ to get $x = \text{\char36}2{,}100$ . Add $\text{\char36}2{,}100$ each year after the first: $\text{\char36}31{,}000$ , $\text{\char36}33{,}100$ , $\text{\char36}35{,}200$ . Sum all three years: $\text{\char36}99{,}300$ .

Mid-gamemedium

Rafael earns $\text{\char36}39{,}500$ in his first year as an assistant coach. He receives the same dollar raise each year and earns $\text{\char36}46{,}700$ in his fifth year. What is the total of Rafael's earnings over his five years on staff?

Subtract the fifth-year salary from the first: $\text{\char36}46{,}700 - \text{\char36}39{,}500 = \text{\char36}7{,}200$ . Over five years there are four equal raises, so divide by $5 - 1 = 4$ to get $x = \text{\char36}1{,}800$ . Add $\text{\char36}1{,}800$ each year after the first: $\text{\char36}39{,}500$ , $\text{\char36}41{,}300$ , $\text{\char36}43{,}100$ , $\text{\char36}44{,}900$ , $\text{\char36}46{,}700$ . Sum all five years: $\text{\char36}215{,}500$ .

Buzzer beatermedium

Naomi earns $\text{\char36}48{,}000$ in her first year as a data analyst. She gets the same dollar raise every year and earns $\text{\char36}54{,}600$ in her fourth year. What is the total of Naomi's earnings during her four years at the company?

Subtract the fourth-year salary from the first: $\text{\char36}54{,}600 - \text{\char36}48{,}000 = \text{\char36}6{,}600$ . Over four years there are three equal raises, so divide by $4 - 1 = 3$ to get $x = \text{\char36}2{,}200$ . Add $\text{\char36}2{,}200$ each year after the first: $\text{\char36}48{,}000$ , $\text{\char36}50{,}200$ , $\text{\char36}52{,}400$ , $\text{\char36}54{,}600$ . Sum all four years: $\text{\char36}205{,}200$ .

Linear raise total earnings. Game on.

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