Solving problems with integers

Worked example 1

(temperature): At midnight the temperature at a camp on Mount Karisimbi was 0 °C. It fell by 2 °C every hour for 4 hours. What was the temperature at 4 a.m.?

1. Falling 2 °C per hour → −2. Four hours → 4.
2. 4 × ( − 2) = −8.
3. The temperature at 4 a.m. was −8 °C.

Worked example 2

(money): Umutoni's phone plan takes 250 Frw from her balance every day. What is the change in her balance after 7 days?

1. Taking money away → −250 per day.
2. 7 × ( − 250) = −1 750.
3. Her balance goes down by 1 750 Frw.

Worked example 3

(depth): A diver in Lake Kivu goes down 36 m in 4 equal stages. What is the change in depth for each stage?

1. Going down 36 m → −36.
2. ( − 36) ÷ 4 = −9.
3. Each stage takes her 9 m deeper (a change of −9 m).

Worked example 4

(profit and loss): A kiosk made a loss of 1 200 Frw every day for 5 days, then a profit of 4 000 Frw every day for 2 days. What was the result for the week?

1. Loss → −1 200; profit → +4 000.
2. 5 × ( − 1 200) = −6 000 and 2 × 4 000 = 8 000.
3. −6 000 + 8 000 = 2 000.
4. For the week the kiosk made a profit of 2 000 Frw.

Worked example 5

(a rate): A fridge cooled from 4 °C to −8 °C in 3 hours, at a steady rate. By how much did the temperature change each hour?

1. Total change: −8 − 4 = −12 °C.
2. ( − 12) ÷ 3 = −4.
3. The temperature went down 4 °C each hour.