How do you solve this?

Question

Joe took twice as long to do his math work than his science work. If he spent 22.5 hours in total over two weeks doing work, how much time did he spend on math and science over those two weeks. [A – 6 marks] a) Define the variables to solve for: Let x represent___________ Let y represent:_________

b) State 2 equations to represent the above information in a linear system and solve the system by elimination or substitution.

The Science Department has quantities of 10% acid solution and 30% acid solution. What volume of each solution to the nearest ml is required to mix together to get 800 ml of a 14% acid solution? [A – 7 marks] a) Define the variables that you want to solve for: Let x represent___________ Let y represent__________

b) State 2 equations to represent the above information in a linear system and solve the system by elimination or substitution.

Answer 1

22.5 = M+S, M=2S

22.5 = 2S +S = 3S

S= 22.5/3 = 7.5 hours on science

M =2S = 15 hours on math

let x=math = M, y=science hours = y

10x + 30(800-x) = 800(14) x=ml of 10, y=800-x = ml of 30%

10x -30x = 11200-24000

20x = 12800

x=12800/20 = 640 ml of 10%

y=800-640 = 160 ml of 30%

.1(640) +.3(160) = 64+48 =112 = 800(.14) = 112