Question

Mrs. Harris' sons are both trying to buy the same hiking backpack. Son #1 has 20 dollars and earns $10.50 per week walking the neighbors dog. Son #2 has 45 dollars and earns $12.00 per week feeding the neighbors multiple animals. After how many weeks will they both have the same amount of money ready to buy the backpack. Write the formula for when both boys will have the same amount of money.

Answer 1

The equation to find when both sons will have the same amount of money is 20 + 10.50w = 45 + 12w. Solving this, we find that the answer yields a negative number of weeks, which is not feasible. Therefore, the two sons will never have the same amount of money based on the given rates of earning.

Step-by-step explanation:

To find out after how many weeks both sons will have the same amount of money to buy the hiking backpack, we need to establish an equation for each son's savings over time. For Son #1, the equation that represents his total money after a certain number of weeks, w, can be expressed as M1 = 20 + 10.50w. Son #2's savings over time can be represented by M2 = 45 + 12w. To find the week they will have the same amount of money, we set these two equations equal to each other:

20 + 10.50w = 45 + 12w

Solving this equation, let's subtract 10.50w from both sides:

20 = 45 + 1.50w

Next, we subtract 45 from both sides:

-25 = 1.50w

Finally, we divide both sides by 1.50 to solve for w:

w = -25 / 1.50

w ≈ -16.67

However, negative weeks do not make sense in this context, which suggests that Son #2 will always have more money than Son #1 as long as they continue earning money at the rates given. So, they will never have the same amount of money at any point in time based on these weekly earnings.