1. Xuxian and Rachel had the same number of marbles. After Rachel gave away 10 marbles and Xuxian gave away 22 marbles, Rachel had 3 times as many marbles as Xuxian. How many marbles did each of them have at first?
2. Mr. Tan put up poles from one end of a road to the other at equal distances apart. There are 27 wooden poles. The width of each pole is 10 cm. The distance etween 2 poles is 30 m. Find the length of the road.
3. Krishnan had 64 coins in his coin box. There were 20-cent coins and 50-cent coins. The total value of all the coins was $ 18.50. How many 20-cent coins and how many 50-cent coins were there?
"Xuxian and Rachel had the same number of marbles."
x = r
"After Rachel gave away 10 marbles and Xuxian gave away 22 marbles, Rachel had 3 times as many marbles as Xuxian."
r-10 = 3(x-22)
x-10 = 3(x-22)
x-10 = 3x-66
2x = 56
x = 28
Rachel and Xuxian each had 28 marbles.
I am assuming that the end poles are centered 5 cm from the ends of the road.
10 cm × 1 meter/(100 cm) = 0.1 m
Each pole is 0.1 meter in diameter.
There are 26 spaces between poles. Each space is 30 meters.
Length of road = 27 poles × 0.1 meter/pole + 26 spaces × 30 meters/space
= 2.7 meters + 780 meters
= 782.7 meters
"Krishnan had 64 coins in his coin box. There were 20-cent coins and 50-cent coins."
t = number of 20-cent coins
f = number of 50-cent coins
t+f = 64
f = 64-t
"The total value of all the coins was 18.50"
0.20t + 0.50f = 18.50
0.20t + 0.50(64-t) = 18.50
0.20t + 32-0.50t = 18.50
-0.30t = -13.50
t = 13.50/0.30 = 45
f = 64-t = 19
There were forty-five 20-cent coins and nineteen 50-cent coins.