If we assume that Lisa is x years old, then Richard will be (x + 6)years
In 5 years time
Lisa = x +5 years
Richard = x +11 years
sum will be 2x + 16 years
4 years ago
Lisa = x-4 years
Richard = x + 2
Sum will be 2x - 2
Therefore;
2(2x-2) = 2x +16
4x -4 = 2x +16
2x = 20
x = 10
Thus, the present age of Lisa is 10 years and that of Richard is 16 years
Answer:
Amount of vinegar. 100% : 20 milliliters
Amount of Italian dressing: 140 milliliters
Step-by-step explanation:
Let's call A the amount of vinegar. 100%
Let's call B the amount of Italian dressing . 12% vinegar
The resulting mixture should have 23% vinegar, and 160 milliliters.
Then we know that the total amount of mixture will be:
![A + B = 160](https://tex.z-dn.net/?f=A%20%2B%20B%20%3D%20160)
Then the total amount of pure antifreeze in the mixture will be:
![A + 0.12B = 0.23 * 160](https://tex.z-dn.net/?f=A%20%2B%200.12B%20%3D%200.23%20%2A%20160)
![A + 0.12B = 36.8](https://tex.z-dn.net/?f=A%20%2B%200.12B%20%3D%2036.8)
Then we have two equations and two unknowns so we solve the system of equations. Multiply the first equation by -1 and add it to the second equation:
![-A -B = -160](https://tex.z-dn.net/?f=-A%20-B%20%3D%20-160)
![-A -B = -160](https://tex.z-dn.net/?f=-A%20-B%20%3D%20-160)
+
![A + 0.12B = 36.8](https://tex.z-dn.net/?f=A%20%2B%200.12B%20%3D%2036.8)
--------------------------------------
![-0.88B = -123.2](https://tex.z-dn.net/?f=-0.88B%20%3D%20-123.2)
![B = \frac{-123.2}{-0.88}](https://tex.z-dn.net/?f=B%20%3D%20%5Cfrac%7B-123.2%7D%7B-0.88%7D)
![B = 140\ milliliters](https://tex.z-dn.net/?f=B%20%3D%20140%5C%20milliliters)
We substitute the value of B into one of the two equations and solve for A.
![A + 140 = 160](https://tex.z-dn.net/?f=A%20%2B%20140%20%3D%20160)
![A = 20\ milliliters](https://tex.z-dn.net/?f=A%20%3D%2020%5C%20milliliters)
(10^2 +10^2)^.5 = 10*(sqrt2)
Answer:
D) y=5x+20
Step-by-step explanation: