3 Soumik has $5 less than his friend Kofi. If they have $97.50 altogether, how much does ea
person have?
4 Two competition winners are to share a prize of $750. If one winner receives twice as mu
as the other, how much will they each receive?
5 A grandfather is six times as old as his grandson. If the grandfather was 45 when his
grandson was born, how old is the grandson?
6 A rectangle of perimeter 74 cm is 7 cm longer than it is wide. What is the length of each sid
7 Smitville is located between Jonesville and Cityville. Smitville is five times as far away from
Cityville as it is from Jonesville. If the distance between Jonesville and Cityville is 288 km,
how far is it from Jonesville to Smitville?
8 Amira is twice as old as her cousin Pam. Nine years ago, their combined age was 18. What
are their present ages?
9 Jabu left town A to travel to town B at 6.00 a.m. He drove at an average speed of 80 km/h.
At 8.30 a.m., Sipho left town A to travel to town B. He drove at an average speed of
100 km/h. At what time will Sipho catch up
with Jabu?
10 Cecelia took 40 minutes to complete a journey. She travelled half the distance at a speed of
100 km/h and the other half at 60 km/h. How far was her journey?
Answers
Step-by-step explanation:
3) Let `S` be the amount of dollars Soumik have, and `K` that Kofi have. "Soumik has `$5` less than his friend Kofi" gives us the equation
`S = K - 5,`
and "they have `$97.50` altogether" gives the equation
`S + K =97.50.`
Substitute `S` from the first equation to the second and get
`K - 5 + K = 97.50,` thus `2K = 97.50 + 5 = 102.50,`
and finally `K = 102.50/2 = 51.25 ($).`
Recall that `S = K - 5` and find `S = 51.25 - 5 = 46.25 ($).`
The answer: Soumik has $46.25 and Kofi has $51.25.
4) Attached above
5) Attached above
6) Attached above
7)
8) Attached above
9) Jabu left town A to travel to town B at 6 am
At 8:30 am, Sipho left town A to travel to town B
Therefore,
6 am to 8 : 30 am = 2 hrs 30 minutes = 2.5 hours
\begin{gathered}Distance = speed \times time\\\\Distance = 80 \times 2.5 = 200\ km\end{gathered}
Distance=speed×time
Distance=80×2.5=200 km
Thus, Jabu went 200 km before Sipho began travel.
Since, both are moving from town A to town B,
Relative speed = 100 - 80 = 20 km/hr
Therefore,
\begin{gathered}Time = \frac{distance}{speed}\\\\Time = \frac{200}{20} = 10\end{gathered}
Time=
speed
distance
Time=
20
200
=10
At 8:30 am, Sipho left town A to travel to town B
Thus Sipho will catch up Jabu at = 8 : 30 am + 10 hours = 6 : 30 pm
Thus Sipho will catch up Jabu at 6 : 30 pm
10) Attached above
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Answer:
Amira is twice as old as her cousin Pam. Nine years ago, their combined age was 18. What
are their present ages?