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Question

These two problems are really confusing me, can someone explain them to me?
1) The Eiffel Tower is 497 ft. taller than the Washington Monument. If each of the monuments were 58 ft shorter, the eiffel tower would be twice as tall as the washington monument. How tall is each?
and...
2) Nine cartons of juice cost the same as 5 fruit cups. Also, one fruit cup costs 50 cents more than one bowl of soup, while one bowl of soup costs 50 cents more than one carton of juice. What would be the cost of each item: a carton of juice, a fruit cup, and a bowl of soup?

Thank you VERY much!

Thnx first answer, im getting it now! But i still need help on the 2nd one

Answer 1

1) Eiffel Tower and Washington monument:

Let x = height of the Eiffel tower, x - 497 = height of Washington monument.

Height of Eiffel tower:
x - 58 = 2(x - 497 - 58)
x - 58 = 2(x - 555)
x - 58 = 2x - 1,110
x = 1,052

Height of Washington monument:
= 1,052 - 497
= 555

Answer: Eiffel Tower is 1,052 ft tall, Washington monument is 555 ft high.

Proof (plug them with their respective height):
1,052 - 58 = 2(555 - 58)
994 = 2 * 497
994 = 994

2) Juice, fruit cups and soup:

Let x = cost per carton of juice, y = cost per fruit cup, z = cost per bowl of soup.

Cost per carton of juice:
9x = 5y
x = 5/9y

Cost per fruit cup:
y = z + $0.50

Cost per bowl of soup:
z = x + $0.50
z = 5/9y + $0.50
z = 5/9(z + $0.50) + $0.50
z = 5/9z + $2.50/9 + $0.50
4/9z = $2.50/9 + $4.50/9
4/9z = $7.00/9
z = $1.75

Cost per fruit cup:
= $1.75 + $0.50
= $2.25

Cost per carton of juice:
= 5/9 * $2.25
= $1.25

Answer: carton of juice = $1.25, cup of fruit = $2.25, bowl of soup = $1.75

Proof (9 cartons of juice cost = 5 fruit cups cost):
9 * $1.25 = 5 * $2.25
$11.25 = $11.25

Answer 2

2) we know that:
9 juices = 5 fruit cups
1 fruit cup is $.50 more than 1 bowl of soup
1 soup is $.50 more than 1 juice

since we know that juice is not more expensive than anything else we'll call it's price x: Juice= x

we can see that soup is $.50 more than juice so: Soup= x + $.50

we know that fruit is $.50 more than soup so: Fruit= x +$.50 + $.50 which is also: Fruit = x+ $1.00

now we go back to 9 juice = 5 fruit cups
lets plug in our x's: 9x = 5(x+$1.00)
distribute the 5 on the right side: 9x= 5x+ $5.00
move the 5x to the other side of the equation: 4x= $5.00
divide both sides by 4: x= $1.25

now that we have x (how much juice costs) we can find the cost of the other items: remember that soup was x+ $.50 so; 1.25+.50= 1.75, and fruit was x +$1.00 so; 1.25 +1.00= 2.25.

so we end up with: juice: $1.25, soup: $1.75, and fruit: $2.25

Answer 3

1) e = w + 497
e - 58 = 2*(w - 58)

This is a system of two equations and two variables; solve normally.

2) 9j = 5c
c = s + 50
s = 50 + j

A system of three equations in three variables; solve normally.