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. ?

the sum of 2 numbers is 20. the greater number is 4 more than the leser number. . what are the 2 numbers?

a garage charged mr. T $48 in parts and $ 36/h in labor . how many hours did the garage spend on mr. t's car if the total bill was $156a?

for the last one i got 3 hours at $36/h = 108

for the 2 numbers that equal 20 i got: 12 + 8 = 20 is that right?

i m stuck on the first 2 can you help?

To find the answer to each question, we can solve them step by step.

1. Question: Lydia sold 4/5 of her candles and has 8 candles left. How many candles did Lydia start with?

To find the number of candles Lydia started with, we need to calculate the total number of candles she sold. Since she sold 4/5 of her candles, we need to subtract that from the total she had before selling to find the remaining 1/5 of her candles (which is equal to 8 candles).

Let's set up an equation to solve it:

(1/5) * Total number of candles = 8

We can solve for the Total number of candles by multiplying both sides of the equation by 5:

Total number of candles = 8 * 5
Total number of candles = 40

Therefore, Lydia started with 40 candles.

2. Question: In a coin purse, there are quarters, dimes, and nickels. There are the same number of dimes as nickels, and half as many quarters as dimes. The total value of the coins is $1.65. How many of each coin are in the coin purse?

Let's represent the number of dimes and nickels as "D" and the number of quarters as "Q". We know that there are the same number of dimes as nickels, so D = N. Also, we know that there are half as many quarters as dimes, so Q = D/2.

To solve this problem, we need to set up an equation for the total value of the coins:

$0.25Q + $0.10D + $0.05N = $1.65

Substituting D = N and Q = D/2, we can rewrite the equation as:

$0.25(D/2) + $0.10D + $0.05D = $1.65

Now we can solve for D:

0.25D/2 + 0.10D + 0.05D = 1.65

Combining like terms, we have:

0.125D + 0.10D + 0.05D = 1.65
0.275D = 1.65

Dividing both sides by 0.275, we find:

D = 1.65 / 0.275
D = 6

Since there are the same number of dimes and nickels, N = D = 6.

And since there are half as many quarters as dimes, Q = D/2 = 6/2 = 3.

Therefore, there are 3 quarters, 6 dimes, and 6 nickels in the coin purse.

3. Question: The sum of two numbers is 20. The greater number is 4 more than the lesser number. What are the two numbers?

Let's represent the two numbers as "x" (lesser number) and "y" (greater number). We know that the sum of the two numbers is 20, so we can set up the equation:

x + y = 20

We also know that the greater number is 4 more than the lesser number, so we can set up another equation:

y = x + 4

Now we can solve this system of equations. We can substitute the second equation into the first equation to eliminate "y":

x + (x + 4) = 20

Simplifying, we have:

2x + 4 = 20

Subtracting 4 from both sides:

2x = 16

Dividing both sides by 2:

x = 8

Now we can substitute this value back into the second equation to find "y":

y = 8 + 4
y = 12

Therefore, the two numbers are 8 and 12.

4. Question: A garage charged Mr. T $48 in parts and $36/h in labor. How many hours did the garage spend on Mr. T's car if the total bill was $156?

Let's represent the number of hours spent on the car as "h". We know that the total bill was $156, with $48 for parts and $36 per hour for labor. So we can set up the equation:

$48 + $36h = $156

Subtracting $48 from both sides:

$36h = $156 - $48
$36h = $108

Dividing both sides by $36:

h = $108 / $36
h = 3

Therefore, the garage spent 3 hours on Mr. T's car.