Cody has 22 rare coins. Each year Cody plans to add 15 coins to his collection. How many years will it take Cody to collect 577 coins?

Question

Determine the correct equation and solution for this situation.

(1 point)
Responses

15 + 22y = 577; 37 years
15 + 22y = 577; 37 years

15y + 22 = 577; 37 years
15y + 22 = 577; 37 years

37y = 577; 16 years
37y = 577; 16 years

7y = 577; 82 years

Answer 1

To determine how many years it will take Cody to collect 577 coins, we can set up the equation based on the information given:

1. Cody starts with 22 coins.
2. He adds 15 coins each year.
3. We need to find the total number of coins after \( y \) years.

The equation can be set up as follows:

\[ \text{Total Coins} = \text{Starting Coins} + \text{Coins Added per Year} \times \text{Number of Years} \]

This can be written as:

\[ 577 = 22 + 15y \]

Now, we solve for \( y \):

1. Subtract 22 from both sides: \[ 577 - 22 = 15y \] \[ 555 = 15y \]

2. Divide both sides by 15: \[ y = \frac{555}{15} \] \[ y = 37 \]

So, it will take Cody 37 years to collect 577 coins.

The correct equation and solution for this situation is:

\[ 15y + 22 = 577; 37 \text{ years} \]

Answer 2

9 of 239 of 23 Items

Question
Tom is given the equation 10x+15=20
to solve. He says the solution is 12
. Which reason justifies his solution?(1 point)
Responses

Tom says that to solve the equation you first divide by 10 and then subtract 15.
Tom says that to solve the equation you first divide by 10 and then subtract 15.

Tom says that to solve the equation you first subtract 15 and then multiply by 10.
Tom says that to solve the equation you first subtract 15 and then multiply by 10.

Tom says that to solve the equation you first add 15 and then divide by 10.
Tom says that to solve the equation you first add 15 and then divide by 10.

Tom says that to solve the equation you first subtract 15 and then divide by 10.
Tom says that to solve the equation you first subtract 15 and then divide by 10.
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Answer 3

To solve the equation \(10x + 15 = 20\), we need to isolate \(x\). Here’s how to do it step by step:

1. Subtract 15 from both sides: \[ 10x + 15 - 15 = 20 - 15 \] This simplifies to: \[ 10x = 5 \]

2. Now, divide both sides by 10: \[ x = \frac{5}{10} \] Simplifying this gives: \[ x = 0.5 \]

Since Tom said that the solution is 12, he made an error in his calculations. The correct reasoning to isolate \(x\) involves both subtracting 15 first and then dividing by 10.

Based on the options given, the correct response that justifies the correct process is:

Tom says that to solve the equation you first subtract 15 and then divide by 10.

Answer 4

Dr. Burrows is measuring the weight of a substance for a science experiment. He added a mystery substance (m) to his experiment. Dr. Burrows used the equation 13.93 + m = 18.0 to find out how much he added. How much of the mystery substance (m) did he add to his experiment?(1 point)
Responses

5.17
5.17

5.07
5.07

4.07
4.07

4.17

Answer 5

To find out how much of the mystery substance \( m \) Dr. Burrows added, we start with the equation:

\[ 13.93 + m = 18.0 \]

To isolate \( m \), we can subtract 13.93 from both sides of the equation:

\[ m = 18.0 - 13.93 \]

Now, calculate \( 18.0 - 13.93 \):

\[ m = 4.07 \]

So, Dr. Burrows added 4.07 of the mystery substance to his experiment.

The correct response is:

4.07

Answer 6

Five times a number added to 10 is 20. What is the number?

Determine the correct equation and the unknown number in this situation.

(1 point)
Responses

5+n+10=20

n = 5

5 plus n plus 10 is equal to 20 n = 5

5(n+10)=20

n = -6

5 times open paren n plus 10 close paren is equal to 20 n = -6

5+10n=20

n = 1.5

5 plus 10 n is equal to 20 n = 1.5

5n+10=20

n = 2

5 n plus 10 is equal to 20 n = 2
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Answer 7

To solve the problem, we start by understanding the statement: "Five times a number added to 10 is 20."

This can be translated into the equation:

\[ 5n + 10 = 20 \]

Now, we will solve for \( n \):

1. Subtract 10 from both sides: \[ 5n = 20 - 10 \] \[ 5n = 10 \]

2. Divide both sides by 5: \[ n = \frac{10}{5} \] \[ n = 2 \]

Thus, the correct equation is \( 5n + 10 = 20 \) and the unknown number \( n \) is \( 2 \).

The correct response is:

5n + 10 = 20; n = 2.

Answer 8

Which graph best represents the solution to

1/4x−6=−4
a number line that goes 0 to 20 and there's a dot on 2.
a number line that goes 0 to 20 and there's a dot on 4
a number line that goes 0 to 20 and there's a dot on 8
a number line that goes 0 to 20 and there's a dot on 10

Answer 9

To solve the equation \( \frac{1}{4}x - 6 = -4 \), we can first isolate \( x \):

1. Start by adding 6 to both sides: \[ \frac{1}{4}x = -4 + 6 \] \[ \frac{1}{4}x = 2 \]

2. Next, multiply both sides by 4 to solve for \( x \): \[ x = 2 \times 4 \] \[ x = 8 \]

The solution to the equation is \( x = 8 \).

Now, based on your options regarding the number line, the graph that best represents the solution will have a dot on 8.

Therefore, the correct response is:

A number line that goes 0 to 20 and there's a dot on 8.

Answer 10

Mariah wants to buy as many collectible dolls as possible, for $4.50 each. If she has $75.00 to spend, how many dolls can she buy? Which equation represents this situation?(1 point)
Responses

75d=4.5
75 d is equal to 4 point 5

d+4.5=75
d plus 4 point 5 is equal to 75

4.5d=75
4 point 5 d is equal to 75

d4.5=75

Answer 11

To determine how many collectible dolls Mariah can buy, we need to formulate an equation based on the given information:

• The cost of each doll is $4.50.
• Mariah has $75.00 to spend.

Let \( d \) represent the number of dolls she can buy. The equation that represents this situation can be set up as follows:

\[ 4.50d = 75 \]

Now, we can solve for \( d \):

1. Divide both sides by 4.50: \[ d = \frac{75}{4.50} \] \[ d = 16.67 \]

Since Mariah cannot buy a fraction of a doll, we round down to the nearest whole number. Therefore, she can buy 16 dolls.

The correct equation that represents this situation is:

4.5d = 75;