Achemist needs 180 milliliters of a 62% solution but she only has 51% and 69% solutions available. calculate how many milliliters of each should be mixed to get the desired result. how many milliliters of the 51% solution should she use?

70 milliliters

Step-by-step explanation:

Let x be the 51% solution and y be the 69% solutions,

Since, the solution after combining them = 180 milliliters

⇒ x + y = 180 (1),

Also, final solution is of 62%,

That is,

51% of x + 69% of y = 62% of 180

0.51x + 0.69y = 0.62 × 180

⇒ 0.51x + 0.69y = 111.6,

⇒ 51x + 69y = 11160 (2),

Equation (2) - 69 × equation (1),

We get,

-18x = -1260

⇒ x = 70

Hence, 70 milliliters of the 51% solution should she use.

The region represents the solution to the given system is region iv.

Step-by-step explanation:

Given : system of linear equation  y = –3x + 5 and y =  0.5x – 1

We have to find the  region that represents the solution to the system.

Consider the given system  

y = –3x + 5 .....(1)

y =  0.5x – 1    ..........(2)

Multiply (2) by 10, we have,

10y = 5x - 10  ....(3)

Multiply equation (1) by 10, we have,

10y = –30x + 50 ..........(4)

Subtract (3) and (4) , we have,

10y - 10y = –30x + 50 - ( 5x - 10 )

Simplify, we have,

0 = –30x + 50 - 5x + 10  

35x = 60

x = (approx)

Put x =  in (3) , we get,

10y = 5 - 10  

Thus, point of solution is (1.71, -0.143)

Since,  (1.71, -0.143) lies in Fourth quadrant.

So the region represents the solution to the given system is region iv.