Mary bought 2 vangaurd sheets each measuring 70 cm by 90 cm. She cut out square cards of identical size from the vangaurd sheets such that there was no wastage.
a) What is the largest possible length she cut out?
b)What is the total number of square cards she cut out such that there was no wastage.
c) If Mary wants to use the cards she cut out as revision card for 8 of her subjects equally, how many cards can she use for each subject? How many cards will be left over?
Write the ratio in simplest form.
20 in : 46 in
(a) GCF(70,90) = 10
(b) 90/10 * 70/10 = 63
(c) 63/8 = 7 with a remainder of 7
To find the answers to these questions, we need to follow these steps:
Step 1: Calculate the largest possible length of the square card
Step 2: Calculate the number of square cards that can be cut out
Step 3: Divide the total number of cards by 8 to find the number of cards for each subject
Step 4: Find the remainder to determine the cards left over
Let's solve each question step by step:
a) What is the largest possible length she cut out?
To find the largest possible length, we need to determine the smallest side length of the rectangle sheets. In this case, the two Vanguard sheets have a length of 70 cm and a width of 90 cm. Since we want to cut out identical square cards with no wastage, the side length of the square card will be the greatest common divisor (GCD) of the two sides of the rectangle sheets.
To find the GCD, we can use the Euclidean algorithm:
Step 1: Set a = 90 and b = 70.
Step 2: Calculate the remainder R when a is divided by b: R = a % b.
Step 3: If R is zero, then the GCD is b. Otherwise, set a = b and b = R, and repeat from Step 2.
Using this algorithm, we have:
Step 1: 90 % 70 = 20
Step 2: Set a = 70 and b = 20
Step 3: 70 % 20 = 10
Step 4: Set a = 20 and b = 10
Step 5: 20 % 10 = 0
Since the remainder has become zero, the GCD is 10 cm. Therefore, the largest possible length that Mary can cut out is 10 cm.
b) What is the total number of square cards she cut out such that there was no wastage?
To find the total number of square cards, we need to divide the area of the rectangle sheets by the area of a single card. The area of a rectangle is calculated by multiplying its length by its width.
In this case, each Vanguard sheet has a length of 70 cm and a width of 90 cm. Thus, the area of each sheet is 70 cm * 90 cm = 6300 cm^2.
Since the square cards have a side length of 10 cm, the area of a single card is 10 cm * 10 cm = 100 cm^2.
To find the total number of square cards, we divide the area of the rectangle sheets by the area of a single card:
Total number of square cards = (Area of rectangle sheets) / (Area of single card)
Total number of square cards = (2 * 6300 cm^2) / (100 cm^2)
Total number of square cards = 126 cards.
Therefore, Mary cut out a total of 126 square cards without any wastage.
c) If Mary wants to use the cards she cut out as revision cards for 8 of her subjects equally, how many cards can she use for each subject? How many cards will be left over?
To determine the number of cards for each subject and the number of cards left over, we divide the total number of square cards by 8 and find the remainder.
Number of cards for each subject = Total number of square cards / 8
Number of cards for each subject = 126 cards / 8
Number of cards for each subject = 15 cards (rounded down to the nearest whole number)
Number of cards left over = Total number of square cards % 8
Number of cards left over = 126 cards % 8
Number of cards left over = 6 cards
Therefore, Mary can use 15 cards for each subject, with 6 cards left over.