Lucy works for a company that manufactures liquid dyes for fabric. she currently wants to mix up some 23%-concentrated teal dye. she has 16 gallons of 15%-concentrated teal dye, as well as plenty of 25%-concentrated teal dye. how many gallons of the 25%-concentrated teal dye will lucy need to add to the 15%-concentrated teal dye to make a batch with a concentration of 23%? gallons

64 gallons

Step-by-step explanation:

Let he mixed x gallons of 25%-concentrated teal dye with 16 gallon of 15%-concentrated teal dye to make 23%-concentrated teal dye.

Thus, the total quantity of the resultant dye = (16+x) gallon

Also,

The concentration of 25%-concentrated teal dye + the concentration of 15%-concentrated teal dye = The concentration of 23%-concentrated teal dye.

⇒ 25 % of x + 15 % of 16 = 23 % ( x + 16 )

⇒ 25 of x + 15 of 16 = 23  ( x + 16 )

⇒ 25 x + 15 × 16 = 23 x +  23 × 16

⇒ 25 x + 240 =  23 x + 368

⇒ 25 x + 240 - 23 x = 368

⇒ 2 x  = 368 - 240

⇒ 2 x  = 128

⇒ x = 64

Hence, the quantity of 25%-concentrated teal dye = 64 gallons

64 Gallons

Step-by-step explanation:

Set up this problem with the same type of table you used in the “concentrated fuel” scenario in the written lesson.

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

the solution is the point

step-by-step explanation:

we have

> equation a

> equation b

adds equation a and equation b

substitute the value of x in equation b to find the value of y

the solution is the point