You have 15 milliliters of a drink that contains 15% milk. how many millimeters of a drink containing 63% milk needs to be added in order to have a final drink that is 45% milk?

4 ml of the 63% milk drink

Step-by-step explanation:

Multiplying 15 ml by 0.15 results in 2.25 ml, the amount of whole milk in the drink.  Let m represent the number of ml of a drink that is 63% milk.

The final amount of milk drink that is to be 45% milk will be 15 ml + m, and the amount of whole milk contained in this drink will be 0.45(15 + m).

Then:

0.15(15 ml) + 0.63(m) = 0.45(15 + m), where m is to be in milliliters.

2.25 + 0.63m = 6.75 + 0.45m

First:  consolidate the m terms on the left.  0.63m less 0.45m yields 18 m; then we have:

2.25 + 18m = 6.75, or

18 m = 4.50, or m = 4 ml.

In conclusion:  adding 4 ml of that 63% milk drink to the initial 15 ml of 15% milk will result in (15 ml + 4 ml) of a 45% milk drink.            

step-by-step explanation:

a) $ 9.50

b) 17

c) y-intercept (0, 12). this is the initial amount of money that joe had prior to playing any game.

d) x-intercept ( 24, 0). this is the number of games that joe will play before he depletes the initial amount of money that he had.

e) slope is -0.5. joe's balance will reduce by 0.5 for every game that he plays.

f)

domain; [0,24]

range; [0,12]

g) x + 2y = 24

step-by-step explanation:

a)

if joe plays 5 games, this will imply that x = 5. substitute x = 5 in the equation and solve for y;

y = -.50x + 12

y = -0.50(5) + 12

y = 9.50

b)

if joe leaves the arcade with $3.50, this will mean that y = 3.50. plug in y = 3.50 in the given equation and solve for x;

y = -.50x + 12

3.50 = -0.50x + 12

0.50x = 12 - 3.50

0.5x = 8.5

x = 17

c)

the function given is   y = -.50x + 12.

the y-intercept is the point where the graph of this function will intersect the y-axis. at this point, the value of x is usually 0. plug in x = 0 in the given equation and determine y;

y = -0.50(0) + 12

y = 12

the y-intercept is thus (0, 12). this is the initial amount of money that joe had prior to playing any game.

d)

the x-intercept refers to the point where the graph of a function intersects with the x-axis. at this point, the value of y is 0. substitute y = 0 in the given equation and solve for x;

0 =   -.50x + 12

0.5x = 12

x = 24

x-intercept ( 24, 0). this is the number of games that joe will play before he depletes the initial amount of money that he had.

e)

the slope of the given equation is -0.5. the equation has been given in slope-intercept form. thus the slope is simply the coefficient of x.

joe's balance will reduce by 0.5 for every game that he plays. this is the interpretation of the slope.

f)

domain is the set of x values for which the function is real and defined. the domain will thus be; [0,24]. this will restrict the balance to only assume positive values.

on the other hand, the range is the set of y values for which a function is real and defined. the range in our case will be [0,12]. joe can have between $0 and $12 balance.

g)

the standard form of the equation of a straight line is;

ax + by = c

where a, b, and c are integers.

our equation is given as;

y = -.50x + 12

re-writing the equation we have;

0.5x + y = 12

divide all through by 0.5;

x + 2y = 24