An orange punch is 45% juice and a mango punch is 20% juice. By combining the two, a company is making 500 L of a fruit punch that is 40% juice. How many liters of orange punch are needed for the company's concoction?

Step-by-step explanation:

step one:

given data

orange punch is 45% juice and

mango punch is 20% juice.

amount of fruit punch to be made is

500 L of a fruit punch that is 40% juice.

Let x = the number of liters of orange punch in the fruit punch.

Then the number of liters of mango is 500 - x

The number of liters of orange + mango juice is

0.45x + 0.2(500 - x), and this must equal the number of liters

in the fruit punch, which is 0.4*500

0.45x + 100 - 0.2x = 200

solve for x

0.45x-0.2x+100-200=0

0.25x-100=0

0.25x = 100

x=100/0.25

x = 400 L

400 L of orange punch

answer: a video game has three difficulty levels: easy, medium, and expert. the game's scoring works in such a way that a player has to score a fixed number of points to advance to the next level, and then the scoring starts over. the total score needed to clear all three difficulty levels is 7,500. two times the number of points needed to clear the easy level is 500 more than the number of points needed to clear the medium level. twice the number of points needed to clear the medium difficulty level is 1,500 more than the number of points needed to clear the expert level. if x, y, and z represent the easy, medium, and expert levels, respectively, and a is the coefficient matrix of the system of equations modeling this situation, identify the inverse matrix, a-1, and the solution matrix, x, of the system of equations.

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