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cody has 22 rare coins. each year clark plans to add 15 to his collection. how many years will it take cody to collect 577 coins?

determine the correct equation and solution for this situation
a. 15+22y=577;37 years
b. 15y+22=577;37 years
c. 37y=577;16 years
d. 7y=577;82 years

9 answers

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

Cody starts with 22 rare coins and adds 15 coins each year. We want to know how many years (let's call that \( y \)) it will take for him to reach a total of 577 coins.

The equation can be set up as follows:

\[ 22 + 15y = 577 \]

This equation states that the initial 22 coins plus 15 coins for each year \( y \) will equal 577 coins.

Now, let's solve for \( y \):

  1. Subtract 22 from both sides:

\[ 15y = 577 - 22 \]

\[ 15y = 555 \]

  1. Divide both sides by 15:

\[ y = \frac{555}{15} \]

\[ y = 37 \]

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

Looking at your options, the correct answer is:

b. \( 15y + 22 = 577; 37 \text{ years} \)

Tom is given the equation 10x+15=20 to solve. He says the solution is 1/2 . Which reason justifies his solution?
a. Tom says that to solve the equation you first divide by 10 and then subtract 15.
b. Tom says that to solve the equation you first subtract 15 and then multiply by 10.
c. Tom says that to solve the equation you first add 15 and then divide by 10.
d. Tom says that to solve the equation you first subtract 15 and then divide by 10.

Let's analyze the equation given:

\[ 10x + 15 = 20 \]

To solve for \( x \), follow these steps:

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

  2. Divide both sides by 10: \[ x = \frac{5}{10} \] \[ x = \frac{1}{2} \]

Now, let's evaluate the options to see which reasoning justifies the solution:

  • a. Tom says that to solve the equation you first divide by 10 and then subtract 15. (Incorrect order)
  • b. Tom says that to solve the equation you first subtract 15 and then multiply by 10. (Incorrect operation)
  • c. Tom says that to solve the equation you first add 15 and then divide by 10. (Incorrect operation)
  • d. Tom says that to solve the equation you first subtract 15 and then divide by 10. (Correct reasoning)

Tom correctly justifies his solution by stating he first subtracts 15 and then divides by 10, leading to the correct result of \( x = \frac{1}{2} \).

Thus, the correct choice is:

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

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?
a. 5.17
b. 5.07
c. 4.07
d. 4.17

To find out how much of the mystery substance (m) Dr. Burrows added to his experiment, we need to solve the equation provided:

\[ 13.93 + m = 18.0 \]

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

\[ m = 18.0 - 13.93 \]

Now, performing the subtraction:

\[ m = 4.07 \]

Thus, the amount of the mystery substance (m) that Dr. Burrows added is:

c. 4.07

5 times a number added to 10 is 20. what is the number?
determine the correct equation and the unknown number in this situation.
a. 5+n+10=20 n=5
b. 5(n+10)=20 n=-6
c. 5+10n=20 n=1.5
d. 5n+10=20 n=2

Let's interpret the problem statement: "5 times a number added to 10 is 20."

We can translate this into a mathematical equation as follows:

\[ 5n + 10 = 20 \]

where \( n \) is the unknown number we want to find.

Now, we need to solve the equation for \( n \):

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

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

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

The correct choice from your options is:

d. \( 5n + 10 = 20 \), \( n = 2 \).

which graph best represents the solution to
1/4x-6=-4
<--•------------------>
<----•---------------->
<--------*------------>
<----------•---------->

To determine which graph best represents the solution to the equation \( \frac{1}{4}x - 6 = -4 \), we first need to solve for \( x \).

  1. Start with the equation: \[ \frac{1}{4}x - 6 = -4 \]

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

  3. Multiply both sides by 4 to solve for \( x \): \[ x = 2 \times 4 \] \[ x = 8 \]

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

Now, to interpret the graphical representations:

  1. A closed circle (•) typically indicates that the value is included in the solution (i.e., it's part of the graph).
  2. An open circle (*) indicates that the value is not included.
  3. The direction of the arrows (if present) or the length of the line indicates whether the solution is less than or greater than \( x = 8 \).

Since the equation \( \frac{1}{4}x - 6 = -4 \) gives us a single point solution \( x = 8 \):

The correct graph would ideally have:

  • A closed circle at \( x = 8 \) (indicating that \( 8 \) is included)
  • A line extending indefinitely in either direction along the x-axis but showing specifically at \( x = 8 \).

Therefore, if you have an option that corresponds to a closed circle at \( x = 8 \) with lines extending outward, that would be the best representation for the solution \( x = 8 \).

Please choose the graph that best fits this description among your options. If you have specific graphs to analyze, please share them, and I can help you select the correct one!