How many fifty-cent pieces are there in the change?
—– answer to question number 3: —– the change is 20.00 – 9.50 = 10.50 let a = # quarters let b = # fifty cent pieces —– number of coins is 30: a + b = 30 total change is 10.50 .25*a + .5*b = 10.5 —– two equations are: a + b = 30 .25*a + 5*b = 10.5 —– we can use substitution as in questions 1 and 2 above, or we can solve as two simultaneous equations by manipulating the equations so one of the unknowns drops out allowing us to solve for the other unknown. we’ll do it the second way this time. —– two equations are: a + b = 30 .25*a + .5*b = 10.5 —– multiply the second equation by 4: a + b = 30 a + 2b = 42 —– subtract first equation from second equation to get: a-a + 2b-b = 42-30 b = 12 —– if b = 12, then a = 18 because a + b = 30 we have: a = 18 b = 12 —– substitute in the second equation to see if we get the right answer: .25*a + .5*b = 10.5 .25*18 + .5*12 = 10.5 4.5 + 6 = 10.5 10.5 = 10.5 —– values are good answer to question number 3 is: there are 12 f
