lydi sold 4/5 of her candles to raise money for the band. she has 8 candles left. how many candles did lydia start with?
a coin purse contains quarters, dimes, and nickes. there are the same number of dimes as nickesl and half as many quarters as dimes. the coins are worth $1.65 . how many of each coin are in the coin purse. ?
for number 1 is it that she had 13candles to start with?
so 1/5 of the candles are left or 8 are left
so she must have had 40 candles
check: 4/5 of 40 = 32
so she has 8 left.
#2. let the number of quarters be x
then the number of dimes is 2x
and the number of nickels is 2x
25x + 10(2x) + 5(2x) = 165
55x = 165
x = 3
there are 3 quarters, 6 dimes and 6 nickels.
check: 3(25) + 6(10) + 6(5) = 165
3(25)+6(10)+6(5)=165
To solve this problem, we need to use algebraic equations.
First, let's denote the number of candles Lydia started with as "x".
From the information given, we know that Lydia sold 4/5 of her candles, which means she has 1/5 of her candles left. So, we can write the equation: (1/5)x = 8.
To solve for x, let's isolate it by multiplying both sides of the equation by 5: x = 8 * 5.
Multiplying, we get x = 40.
Therefore, Lydia started with 40 candles.
Now let's move on to the second problem:
Let's denote the number of dimes as "D", the number of nickels as "N", and the number of quarters as "Q".
According to the given information, we have three conditions:
1. There are the same number of dimes as nickels: N = D.
2. There are half as many quarters as dimes: Q = D/2.
3. The coins are worth $1.65: $0.25Q + $0.10D + $0.05N = $1.65.
Using the first condition, we can substitute N for D in the third condition to get: $0.10D + $0.05D + $0.05D = $1.65.
Simplifying the equation, we have: $0.20D = $1.65.
Now let's solve for D by dividing both sides of the equation by $0.20: D = $1.65 / $0.20.
Dividing, we get D = 8.25.
However, since we can't have a fraction of a coin, we need to adjust the values. Since there cannot be a fraction of dimes or nickels, we need to check if there is a solution where D could be equal to 8, rather than 8.25.
With D = 8, we can solve for N using the second condition: N = D = 8.
And we can solve for Q using the third condition: $0.25Q + $0.10D + $0.05N = $1.65.
By substituting the known values, we get: $0.25Q + $0.10(8) + $0.05(8) = $1.65.
Simplifying, we have: $0.25Q + $0.80 + $0.40 = $1.65.
Combining like terms, we get: $0.25Q + $1.20 = $1.65.
Subtracting $1.20 from both sides of the equation, we get: $0.25Q = $1.65 - $1.20.
Simplifying, we have: $0.25Q = $0.45.
To solve for Q, we divide both sides of the equation by $0.25: Q = $0.45 / $0.25.
Dividing, we get Q = 1.8.
However, since quarters cannot have fractions, we see that D = 8 and N = 8 do not satisfy the conditions stated in the problem.
Therefore, there is no whole number solution to this problem.