Your piggy bank contains $19.75 in dimes and quarters. There are 100 coins in all. How many dimes are there?
2 answers:
<span>Let x = be the number of dimes and y = number of quarters.
Since the total number of coins is 100, x + y = 100.
Since the total is cent value is 19.75, comprised of .10 for dimes and .25 for quarters, we have .10x + .25y = 19.75.
This is just a system of equations. Solve one of the dozen ways that work for solving systems of linear equations.
Using substitution:
x = 100 - y
Plug this into the other equation
.10 (100 - y) + .25 y = 19.75
10 - .10 y + .25 y = 19.75
10 + .15y = 19.75
.15 y = 9.75
y = 65
So there are 65 quarters. Since x + y = 100, there must be 35 dimes.</span><span>Hope This Helps</span>
D = no. of dimes
q = no. of quarters
$total equation
.10d + .25q = 19.75
No. of coins equation
d + q = 100
d = (100-q)
Replace d
with (100-q) in the $total equation
.10(100-q) + .25q = 19.75
10 - .10q + .25q = 19.75
10.15 q = 9.75
q =
q = 65 quarters
100 - 65 =
35 dimes.
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∡A+∡B+∡C=180°
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triangle ABC and triangle XYZ are similar
so
∡X=∡A
∡Y=∡B
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hence
∡Z=30°
the answer is∡Z=30°
