Achemist needs 120 milliliters of a 72% solution but has only 51% and 87% solutions available. find how many milliliters of each that should be mixed to get the desired solution.

The chemist needs 50 mL of 51% solution and 70 mL of 87% solution.

Step-by-step explanation:

If x is the volume of 51% solution, and y is the volume of 87% solution, then:

x + y = 120

0.51x + 0.87y = 0.72(120)

Solve the system of equations.

0.51x + 0.87(120 − x) = 0.72(120)

0.51x + 104.4 − 0.87x = 86.4

0.36x = 18

x = 50

y = 70

The chemist needs 50 mL of 51% solution and 70 mL of 87% solution.

5x + 3y = - 4

step-by-step explanation:

the equation of a line in standard form is

ax + by = c ( a is a positive integer and b, c are integers )

express the line first of all in slope- intercept form

y = mx + c ( m is the slope and c the y-intercept )

to calculate m use the gradient formula

m = ( y₂ - y₁ ) / ( x₂ - x₁ )

with (x₁, y₁ ) = (7, - 3) and (x₂, y₂ ) = (4, - 8)

m = = -

y = - x + c ← is the partial equation

to find c substitute either of the 2 points into the partial equation

using (4, - 8 ), then

- 8 = - + c ⇒ c = -

y = - x - ← in slope-intercept form

multiply all terms by 3 to eliminate the fractions

3y = - 5x - 4 ( add 5x to both sides )

5x + 3y = - 4 ← in standard form

1st integer x

2nd integer x+1

3rd integer x+2

4th integer x+3

x+x+1 +x+2+x+3 =74

combine like terms

4x+6 = 74

subtract 6 from each side

4x = 68

x = 17

the integers are 17,18,19,20