I. Given below is a magic square. Place the number in the appropriate square so that in each row, column, and diagonal the sums are equal.
| 32/38 | 18/38 | 4/38 | -14/-38 |
|---|---|---|---|
| -18/-57 | ? | ? | 104/152 |
| 22/38 | ? | ? | -20/-95 |
| 1/19 | -16/-38 | 45/57 | 60/114 |
II. Choose the correct answer:
1. A tank holds 45.5 liters of water. If 2/5 of the water is used, how many liters of water remain in the tank?
(a) 18.2 liters
(b) 27.3 liters
(c) 20 liters
(d) 30 liters
2. A runner jogs 2/3 of a mile every day for 4 days. How many miles does the runner jog in total?
(a) 8/3
(b) 4/3
(c) 2 miles
(d) 5/2
3. Maria buys 3.5 pounds of apples at $2.20 per pound and 2 pounds of oranges at $3 per pound. How much does she spend in total?
(a) $7.70
(b) $13.90
(c) $10.50
(d) $13.70
4. A rectangular garden has a length of 12.5 feet and a width of 8.75 feet. What is the area of the garden?
(a) 110 square feet
(b) 108.25 square feet
(c) 109.375 square feet
(d) 111.5 square feet
5. A cyclist travels 5.8 miles in the first hour, 4.25 miles in the second hour, and 6.5 miles in the third hour. How far does the cyclist travel in total?
(a) 16.55 miles
(b) 16.5 miles
(c) 16.75 miles
(d) 17 miles
Answer (2)
I. To solve the magic square problem, we need to ensure that the sum of each row, column, and diagonal are equal. Each number in the cell is given, and we will find the missing numbers marked by '?'. The typical approach is to determine the magic constant, which is the sum that each row, column, or diagonal will equal.
For a 4x4 magic square, the magic constant (M) can be calculated using the formula:
M = n sum of all numbers
However, without complete numbers or a way to sum, let's solve with available logical reasoning (typically counting sequence or balancing method) or refer to specific inputs if further detailed numbers are provided.
II. Solutions to the multiple-choice questions:
Tank Problem:
Total volume: 45.5 liters.
Water used: 5 2 × 45.5 = 18.2 liters.
Remaining water: 45.5 − 18.2 = 27.3 liters.
The correct answer is (b) 27.3 liters.
Runner Problem:
Jogged daily: 3 2 of a mile.
For 4 days: 4 × 3 2 = 3 8 miles.
Convert into a mixed number: 2 3 2 miles.
The correct answer is (a) 8/3.
Maria's Purchase:
Cost of apples: 3.5 × 2.20 = 7.70 dollars.
Cost of oranges: 2 × 3 = 6 dollars.
Total cost: 7.70 + 6 = 13.70 dollars.
The correct answer is (d) $13.70.
Garden Area:
Length = 12.5 feet, Width = 8.75 feet.
Area = length × width = 12.5 × 8.75 = 109.375 square feet.
The correct answer is (c) 109.375 square feet.
Cyclist Travel:
Travel in 1st hour: 5.8 miles.
Travel in 2nd hour: 4.25 miles.
Travel in 3rd hour: 6.5 miles.
Total travel = 5.8 + 4.25 + 6.5 = 16.55 miles.
The correct answer is (a) 16.55 miles.
To solve the magic square, ensure each row, column, and diagonal equals 34. For the multiple-choice questions, answers are: 1. (b) 27.3 liters, 2. (a) 8/3, 3. (d) $13.70, 4. (c) 109.375 square feet, 5. (a) 16.55 miles.
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