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algol13
3 years ago
12

a postcard has an area of 24 square inches. two enlargements of the postcard have areas of 54 square inches and 96 square inches

. in each postcard the length is 1 and 1/2 times the width. what could be the dimensions of the postcard or the enlargements.
Mathematics
2 answers:
LekaFEV [45]3 years ago
6 0
So,

The length is always 1.5 times the width.

l = 1.5w

lw = 24
lw = 54
lw = 96

Or, we could put it this way:
1.5w(w) = 24
1.5w(w) = 54
1.5w(w) = 96

So,
1.5w^2=24
1.5w^2=54
1.5w^2=96

Dividing both sides by 1.5, we get:
w^2 = 16
w^2 = 36
w^2 = 64

And solving for the only logical dimension, we get:
w = 4
w = 6
w = 8

And their corresponding lengths:
l = 1.5(4) = 6
l = 1.5(6) = 9
l = 1.5(8) = 12

So a few lengths could be:
(l,w)
(6,4)
(9,6)
(12,8)

Of course, there are infinite solutions.
lorasvet [3.4K]3 years ago
5 0
4 and 6 is the original. The 54 inch one is 6 and 9. The 96 inch one is 8 and 12
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Max has 5.50. He has eight more quarters than he does nickels. He had four times as many dimes as he has nickels. How many quart
Oliga [24]

Answer:

<h2>There are 13 quarters, 5 nickels and 20 dimes.</h2>

Step-by-step explanation:

Givens

  • Max has $5.50.
  • He has eight more quarters than he does nickels.
  • He had four times as many dimes as he has nickels.

From these statements, we can deduce algebraical expressions to solve the problem. Let's call q quarters, n nickels and d dimes.

q=n+8 (8 more quarters than nickels)

d=4n (he has four times as many dimes as he has nickels).

0.25q+0.05n+0.10d=5.50 (Max has a total of $5.50, one quartes is $0.25, one nickel is $0.05 and one dime is $0.10).

Let's replace the first two expressions into the third equation

0.25(n+8)+0.05n+0.10(4n)=5.50\\0.25n+2+0.05n+0.40n=5.50\\0.70n=5.50-2\\n=\frac{3.50}{0.70}\\ n=5

There are 5 nickels.

Now, we use this value to find the number of quarters

q=5+8=13

There are 13 quarters.

Also, d=4(5)=20

There are 20 dimes.

Therefore, there are 13 quarters, 5 nickels and 20 dimes.

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