Round 1
Solve each equation.
12/x = 1.8/6
x = 40
Solve each equation.
x+2 5
__________ = _______
4 3
14
x = _____
3
Solve each equation.
2x 4.5
__________ = _______
3 4
27
x = _____
16
An ice cream machine produced 44 ice creams per minute. After reconditioning, its speed increased to 55 ice creams per minute. By what percent did the speed of the machine increase?
25%
In a two-digit number, the tens digit is two less than the units digit. If the digits are reversed, the sum of the reversed number and the original number is 154. Find the original number.
68
An alloy is composed of nickel, zinc, and copper in a ratio of 7:2:9. How many kilograms of each metal are needed to make 3.6 kg of this alloy?
1.4 kg of nickel, 0.4 kg of zinc, 1.8 kg of copper
A mill processes 48 tons of flour in 3 hours. How many tons of flour can the mill process in 8 hours if its rate or production stays the same?
128 tons of flour
The shipment of 27 boxes containing 8 lbs of flour each was repackaged in 24 larger boxes. How many pounds did each of these boxes contain?
9 lb
Ying Zyiyu covers the first 300 miles of a trip traveling at 60 mph. and the last hundred miles traveling at 40 mph. What was his average speed for the entire trip?
53 1/3 mph
Ria is 6 years older than her brother. Fourteen years ago, she was twice as old as he was. How old is each now?
Ria is 26 years old.
Her brother is 20 years old.
Find the number if:
6% of it is 27
450
Find the number if:
4.5% of it is 23% of 45
230
Before a sale, an item’s price was $38.00; during the sale, it was 15% off. What was the sale price?
$32.30
Solve each equation.
|x−2|=6
x = 8, x = −4
In Aunt Melly’s attics there are also spiders and ants, the total of 136 legs and 20 heads. If a spider has 8 legs and an ant has 6 legs, how many spiders and how many ants are there?
8 spiders and 12 ants
By what percent will the product of two numbers decrease if one of them is decreased by 25% and the other is decreased by 50%?
62.5%
How many percent is the change in the price, if:
The price was $75 and now it is $300?
The price is increased by 300 %
How many percent is the change in the price, if:
The price was $160 and now it is $40?
The price is decreased by 75 %
Solve each equation.
6 2
__________ = _______
3x+2 5
x = 13/3 or x = 4 1/3
Fresh raspberries contain 80% water. Dried raspberries contain only 20% water. How many pounds of dried raspberries do you get from 36 lb of fresh berries?
9 lb of dried raspberries
Solve each equation.
3(x−0.2)=1.8+x
x = 1.2
Kate had 70 brooms; Alisa had 20 more brooms than Kate. What was the ratio of Kate’s brooms to Alisa’s brooms?
7 : 9
Initially, the ratio of Alex’s toy cars to Pete’s toy cars was 7:3. After Alex gave 20 toy cars to Pete, they had each an equal number of cars. How many toy cars did they have altogether?
100toys
This morning, some dragons, horses, and chickens were playing in my backyard. I counted 15 heads, 50 legs, and 4 wings. How many dragons, how many horses, and how many chickens were playing in my backyard? (For your information: any healthy dragon has three heads, four legs, and two wings. Feel free to use Wikipedia to obtain the information about the number of heads, legs, and wings of the rest of the creatures. Oh, and all creatures on my backyard were healthy.)
1 dragon, 11 horses, 1 chicken
Solve each equation.
4.5 12.5
______= _______
y 4
y = 1.44