You want to draw an enlargement of a design that is printed on a card that is 5in by 6in. You will be drawing this design on a piece of paper that is 8 1/2 by 11 in. What are the dimensions of the largest complete enlargement that you can make?
The ratio of the dimensions of the design on the card is 5:6.
To find the dimensions of the largest complete enlargement, we need to find the ratio between the dimensions of the available paper and the dimensions of the design on the card.
The ratio between the width of the paper (8 1/2 inches) and the width of the design on the card (5 inches) is:
(8 1/2) / 5 = 17/2 / 5 = (17/2) * (1/5) = 17/10
The ratio between the height of the paper (11 inches) and the height of the design on the card (6 inches) is:
11 / 6 = (11/1) * (1/6) = 11/6
To maintain the same aspect ratio as the design on the card, the dimensions of the largest complete enlargement must have the same ratio.
Let's assume the width of the largest complete enlargement is W inches.
Then, the height of the largest complete enlargement will be (W * 6/5) inches, as the aspect ratio must be maintained.
To find the largest complete enlargement, we need to set up a proportion:
W / (W * 6/5) = 17/10
Cross-multiplying and simplifying:
W / (6W/5) = 17/10
5W = (6W/5) * (17/10)
5W = 102W/50
50 * 5W = 102W
250W = 102W
148W = 0
W = 0
From the proportion, we have W = 0, which is not a valid dimension.
Therefore, it is not possible to create a complete enlargement on the available paper since the aspect ratio differs.