Really hard math algebra question?
To answer this question you MUST create an algebraic formula that includes all the information given. I will not get marks if I did trial and error.
There’s a box with 30 coins in it. The total value of all the coins combined is .75. There are also only quarters and loonies ( dollar bills if your not Canadian) inside the box.
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(Solving in cents)
Number of quarters = x
Number of loonies = y
25x + 100y = 1275…eqn 1
x + y = 30 (total of 30 coins)
x = 30-y…eqn 2
Plug in the value of x from eqn 1 into eqn 2:
25(30-y) + 100y = 1275
750-25y+100y = 1275
75y = 525
y = 7
Therefore:
# of quarters (30-y) = 30-7 = 23
# of loonies (y) = 7
Check:
7 loonies = $7
23 quarters = 23*0.25 = $5.75
Total = $12.75…which checks out with the question.
Q = number of quarters
D = number of dollars
Q + D = 30
Q = 30 − D … equation 1
(0.25)Q + (1)D = 12.75 … equation 2
Substitute equation 1 into equation 2:
(0.25)(30 − D) + (1)D = 12.75
7.5 − (0.25)D + D = 12.75
(0.75)D = 5.25
D = 7 … dollars or loonies
Q = 30 − D … equation 1
Q = 30 − 7
Q = 23 … quarters