Y = 2(6 + 1) + 5(3 + 2)
1 answer:
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Recall your d = rt, distance = rate * time
let's say the boat's rate is "b" in still water, and the current's rate is "c"
as the boat goes upstream, is not really going "b" fast, the water is not still anyway, is going much slower, is going " b - c ", because the current's rate is eroding speed because is going against the current.
as the boat goes downstream, is not going "b" fast either, is going faster, is going " b + c " fast, because is going downstream and thus with the current and the current is adding speed to it. notice, it takes longer going up, 5hrs, then coming down, 3hrs, same 150 on each way.
solve for "r"
what's the boat's rate? well, 30+r = b
let's say the boat's rate is "b" in still water, and the current's rate is "c"
as the boat goes upstream, is not really going "b" fast, the water is not still anyway, is going much slower, is going " b - c ", because the current's rate is eroding speed because is going against the current.
as the boat goes downstream, is not going "b" fast either, is going faster, is going " b + c " fast, because is going downstream and thus with the current and the current is adding speed to it. notice, it takes longer going up, 5hrs, then coming down, 3hrs, same 150 on each way.
solve for "r"
what's the boat's rate? well, 30+r = b
Answer:
You have 15 dimes. You have 9 quarters. You have 12 nickels
Step-by-step explanation:
lets set some variables:
let "n" = the number of nickels
let "d" = the number of dimes
let "q" = the number of quarters
So, the total amount of money you have should be: $4.35 = 0.25q + 0.10d + 0.05n
Now let's look at the relationships between the coins:
"There are three fewer quarters than nickels": n - 3 = q
"six more dimes than quarters": q + 6 = d
So now you have three equations with three variables, all you need to do is solve.
first, you can substitute "n-3" for "q" (according to the 2nd equation) in the 1st and 3rd equation, you get:
You now only have two equations and two variables.
Simplify:
Now substitute "n+3" for "d" (according to the 2nd equation) in the 1st equation:
4.35=0.30n-0.75+0.10(n+3)
simplify:
4.35=0.30n-0.75+0.10n+0.30
4.35=0.40n-0.45
4.35+0.45=0.40n
4.80=0.40n
n=12
You have 12 nickels. Now sub "n" back into your equations to find the number of dimes and quarters:
n - 3 = q
12 - 3 = q
q = 9
You have 9 quarters.
q + 6 = d
9 + 6 = d
d = 15
You have 15 dimes.