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amm1812
3 years ago
9

Solve for x if 25^x+2=125^3x+4

Mathematics
2 answers:
bogdanovich [222]3 years ago
6 0
This one was pretty tough but Math way helped, you should try it out, it explains the problems so you can learn it. I got x = 0, 5
igomit [66]3 years ago
4 0
What you want to do is write the numbers with similar bases, and then you can cross the bases off. Like this:

25^x+2=125^3x+4
5^2(x+2)=5^3(3x+4)
Now you can cross the similar bases off.
2(x+2)=3(3x+4)
2x+4=9x+12
7x=-8
X=-8/7
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You manage an ice cream factory that makes two flavors: Creamy Vanilla and Continental Mocha. Into each quart of Creamy Vanilla
Mars2501 [29]

Answer:

You should make 250 quarts of Creamy Vanilla and 200 of Continental Mocha to use up all the eggs and cream.

Step-by-step explanation:

This problem can be solved by a first order equation

I am going to call x the number of quarts of Creamy Vanilla and y the number of quarts of Continental Mocha.

The problem states that each quart of Creamy Vanilla uses 2 eggs and each quart of Continental Mocha uses 1 egg. There are 700 eggs in stock, so:

2x + y = 700.

The problem also states that each quart of Creamy Vanilla uses 3 cups of cream and that each quart of Continental Mocha uses 3 cups of cream. There are 1350 cups of cream in stock, so:

3x + 3y = 1350

Now we have to solve the following system of equations

1) 2x + y = 700

2) 3x + 3y = 1350

I am going to write y as function of x in 1) and replace it in 2)

y = 700 - 2x

3x + 3(700 - 2x) = 1350

3x + 2100 - 6x = 1350

-3x = -750 *(-1)

3x = 750

x = 250

You should make 250 quarts of Creamy Vanilla

Now, replace it in 1)

y = 700 - 2x

y = 700 - 2(250)

y = 700 - 500

y = 200.

You should make 200 quarts of Continental Mocha

7 0
3 years ago
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