The total if all 236 coins were nickels would be $11.80, which is $3.95 short of the actual amount.
Replacing a nickel with a dime adds $0.05 to the total value, so there must have been $3.95/$0.05 = 79 such replacements.
There are 79 dimes.
There are 236 -79 = 157 nickels.
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Using the given variables, the problem statement gives rise to two equations. One is the based on the number of coins. The other is based on their value.
- n + d = 236
- .05n +.10d = 15.75
Solving the first for n, we get
... n = 236 - d
Substituting that into the second equation, we have
... .05(236 -d) +.10d = 15.75
... .05d = 15.75 -236·.05 . . . . . collect terms, subtract .05·236
... d = 3.95/.05 . . . . . . . . . . . . . divide by .05
... d = 79
... n = 236-79 = 157
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The solution should look familiar, as it matches the verbal description at the beginning.
Y = kx is the direct variation equation with k being the "constant of variation"
The constant here being the conversion decimal .91
y = 0.91x
Hope this helps!
Distributive property
-8*4=-32 -8*9x=-72x
-32-72x=7(-2-11x)
7(-2)=-14 7(-11x)=-77x
-32-72x=-14-77x
Combine Like Terms
-32+14=-18 -77x+72x=-5x
-18=-5x
Divide both sides by -5 and theres your answer
Answer:
y=-1x+3
y-2=3(x-1)
Step-by-step explanation:
Slope: -1
y-intercept: 3
Answer: the speed of the plane is 300 miles per hour
The strength of the tail wind is 400 miles per hour
Step-by-step explanation:
A tail wind travels in the direction of the airplane. It took the plane 3 hours to travel 2100 miles with a tail wind.
Speed = distance / time
The speed of the airplane while travelling with the tail wind is
2100/3 = 700 miles per hour.
It took the plane 7 hours to make the return trip against the wind. This means that the plane travelled the same distance of 2100 miles back in 7 hours.
The speed of the plane while travelling back would be
2100/7 = 300 miles per hour
The speed of the wind would be
the speed while it was flying with the tail wind - the speed when it was flying against the tail wind . it becomes
700-300 = 400 miles per hour