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ser-zykov [4K]
3 years ago
5

A paint company mixes it's paint with water to create more paint per gallon. They currently have ten gallon jugs which contain 1

0% water. How much water must they add to create a 80/20 mix of paint to water?
Mathematics
1 answer:
Karo-lina-s [1.5K]3 years ago
5 0
<h3>Answer:  1.25 gallons</h3>

==================================

Explanation:

They currently have ten gallon jugs that contain 10% water, so this means 0.10*10 = 1 gallon of the jug is water and the other 10-1 = 9 gallons is paint. This is assuming the cans are just paint and water.

The ratio of paint to water is 90:10 which reduces to 9:1

Often it helps to reduce as much as possible, but it's actually more handy in this case to keep it at 90:10 so you can see the two parts add back up to 100%

--------------

Let x be the amount of water we add. This amount is in gallons.

We start off with 1 gallon of water and it bumps up to 1+x gallons of water.

The overall amount of 10 gallons also bumps up to 10+x gallons.

We want a ratio of 80:20 this time, so we want 20 parts water and 80 parts paint. In other words, we want 20/(20+80) = 20/100 = 20% water

Divide (1+x) over (10+x) to get (1+x)/(10+x). This represents the fraction of water. We want this fraction to be equal to 0.20, which is the 20% water amount. It is also equal to 20/100.

--------------

(1+x)/(10+x) = 20/100

100(1+x) = 20(10+x) ... cross multiply

100+100x = 200+20x ... distribute

100x-20x = 200-100

80x = 100

x = 100/80 ... divide both sides by 80

x = 1.25

You need to add 1.25 gallons of water

--------------

If you add 1.25 gallons of water, then,

amount of water = 1+x = 1+1.25 = 2.25

amount of paint&water = 10+x = 10+1.25 = 11.25

So you'll have 2.25 gallons of water out of 11.25 gallons of water&paint mix

2.25/11.25 = 0.2 = 20% water

This confirms our answer.

--------------

Extra info:

1.25 gallons = 1 gallon + 1/4 gallon

1.25 gallons = 1 gallon + 1 quart

This is because 1 gallon = 4 quarts, so 1 quart = 1/4 gallon.

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A baseball team can spend up to $1500 on bats. Bats cost $32 each. Which inequality represents the number of bats b they can buy
Katena32 [7]

Answer:

32b<1500

Step-by-step explanation:

a. the can spend up to 1500 but not more so it has to be less

b= 46 bats

46x32= 1472<1500

6 0
2 years ago
Type the correct answer in the box. Use numerals instead of words. If necessary, use / for the fraction bar.
pantera1 [17]

Answer:

-5/2 x -33/4

Step-by-step explanation:

(-11/2 x + 3) -2 (-11/4 x -5/2)

(-11/2 x + 3/1) -2 (-11/4 x -5/2)

The LCM of 2 and 1 is 2, and the LCM of 4 and 2 is 4.

(-11/2 x + 6/2) -2 (-11/4 x -20/4)

( -5/2x) -2 (-31/4)

-5/2x -2 -31/4

-5/2x -2/1 -31/4

LCM of -2 -31/4 is 4

-2/4 -31/4

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-5/2x -33/4 in simplest form.

4 0
2 years ago
Calculate the area of a square with sides of 5 inches.
Luda [366]

Answer:

A = 25 in²

General Formulas and Concepts:

<u>Pre-Algebra</u>

  • Order of Operations: BPEMDAS

<u>Geometry</u>

  • Area of a Square: A = x²

Step-by-step explanation:

<u>Step 1: Define</u>

Side length = 5 in

<u>Step 2: Solve for </u><em><u>A</u></em>

  1. Substitute:                    A = (5 in)²
  2. Evaluate:                       A = 25 in²

And we have our final answer!

6 0
2 years ago
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Solve the following system of inequalities graphically on the set of axes below. State
Serhud [2]

Answer:

(x,y) = (-1,1)

Step-by-step explanation:

Given

y>-2x - 1

y>x + 2

Required

Solve graphically

See attachment for graph;

The black shade represents y>-2x - 1

While the green, represents y>x + 2

Next, determine the intersection points between the two lines

From the attached graph, we have:

(x,y) = (-1,1)

<em>Hence, the solution is:</em>(-1,1)

8 0
2 years ago
Mattie Evans drove 350 miles in the same amount of time that it took a turbo propeller plane to travel 1200 miles. The speed of
frosja888 [35]

The speed of the plane will be equal to 240 Mph.

<h3>What is speed?</h3>

Speed is defined as the ratio of the time distance travelled by the body to the time taken by the body to cover the distance.

Given that:-

  • Mattie Evans drove 350 miles in the same amount of time that it took a turbo propeller plane to travel 1200 miles.
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The speed of the plane will be calculated as:-

Let the speed of the car will be x mph so the speed of the plane will be

(x + 170)

Now time for the plane:-

Tp = Dp / Sp

Tp = 1200 / (x+170)

Now time for the car:-

Tc = Dc / Sc

Tc = 350 / x

It is given that time taken by both the plane and the car are equal:-

Tp  =  Tc

1200 / x+170 = 350 / x

1200x = 350x +  59500

850x  = 59500

x  =  59500 / 850

x  =  70mph

The speed of the plane will be calculated By:-

Sp = x + 170 = 70 + 170 = 240 Mph

Therefore the speed of the plane will be equal to 240 Mph.

To know more about Speed follow

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