Jemima has three boxes with a total weight of 5115 kg. Box B weighs 512 kg more than box A and box C weighs 315 kg more than box B. Choose the correct statement:
2115
Michelle has a budget of 3900 to purchase paperback books and hard cover books for her classroom. She wants the number of hard cover to be least five more than or three times the number of paperback books
To find the correct statement, let's represent the weights of the three boxes:
Let the weight of box A be x kg.
Then, the weight of box B would be (x + 512) kg (512 kg more than box A).
And the weight of box C would be [(x + 512) + 315] kg (315 kg more than box B).
According to the given information, the sum of the weights of all three boxes is 5115 kg.
So, our equation becomes:
x + (x + 512) + [(x + 512) + 315] = 5115
Simplifying the equation:
3x + 1339 = 5115
Now, solving for x:
3x = 5115 - 1339
3x = 3776
x = 3776 / 3
x ≈ 1258.67
Since box weights are usually measured in whole numbers, we need to select the closest possible whole number for box A. That would be 1259 kg.
Now, let's check the statements:
Statement 1: Box A weighs 1259 kg.
Statement 2: Box B weighs 1771 kg (1259 + 512).
Statement 3: Box C weighs 2086 kg (1771 + 315).
Now, let's verify if the total weight of the three boxes adds up to 5115 kg as given:
1259 + 1771 + 2086 = 5116 kg
Since the sum of the weights is not equal to 5115 kg, none of the statements are correct.
To solve this problem, we need to set up a system of equations. Let's assign variables to the weights of the boxes:
Let's say the weight of box A is x kg.
Then, the weight of box B is (x + 512) kg, as it weighs 512 kg more than box A.
Similarly, the weight of box C is (x + 512 + 315) kg, as it weighs 315 kg more than box B.
According to the given information, the total weight of the three boxes is 5115 kg. So, we can write the equation:
x + (x + 512) + (x + 512 + 315) = 5115
Now, we can solve this equation to determine the weight of box A, and then find the correct statement.
Let's simplify the equation:
3x + 1339 = 5115
Next, let's isolate the x variable by subtracting 1339 from both sides of the equation:
3x = 5115 - 1339
3x = 3776
Finally, divide both sides of the equation by 3 to find the value of x:
x = 3776 / 3
x = 1258.67
Since the weight of the boxes should be in kilograms, we can round the weight of box A to the nearest whole number:
x ≈ 1259 kg
Now that we have found the weight of box A, we can determine the weights of boxes B and C:
Box B: x + 512 = 1259 + 512 = 1771 kg
Box C: x + 512 + 315 = 1259 + 512 + 315 = 2086 kg
Now we can check the statements:
A) Box A weighs 1259 kg -- This is true based on our calculations.
B) Box B weighs 2086 kg -- This is false. Box B actually weighs 1771 kg.
C) Box C weighs 1568 kg -- This is false. Box C actually weighs 2086 kg.
D) Box A weighs 1371 kg -- This is false. Box A actually weighs 1259 kg.
Therefore, the correct statement is A) Box A weighs 1259 kg.