Question

Elliott is counting the change from a class fundraiser. He has half as many quarters as nickels, and he has 7 fewer dimes than nickels. The total value of coins is $5.90. He wrote the equation 0 Which statements identify Elliott’s errors? Check all that apply. He should have written the expression for the number of dimes as x – 7. He should have written the coin values as 5, 10, and 25 and not as 0.5, 0.10, and 0.25. He should have written the coin value for the nickel as 0.05. He should have translated the scenario as value of all dimes = value of all nickels and value of all quarters = value of all nickels. He should have written the expression for number of nickels as 2x.

Answer 1

The equation written by Elliot, which was not included in the question, is:

$0.10(7-x)+0.5(x)+0.25(0.5x)=5.90$

The statements from which you have to identify the errors are:

a) He should have written the expression for the number of dimes as x – 7.

b) He should have written the coin values as 5, 10, and 25 and not as 0.5, 0.10, and 0.25.

c) He should have written the coin value for the nickel as 0.05.

d) He should have translated the scenario as the value of all dimes = value of all nickels and value of all quarters = value of all nickels.

e) He should have written the expression for the number of nickels as 2x.

Answer:

There two errors:

• First statement: He should have written the expression for the number of dimes as x - 7.

• Third statement: He should have written the coin value for the nickel as 0.05

Explanation:

I will start by writing the correct expression following the statements step-by-step:

1) He has half as many quarters as nickels

• Name x the number of nickels: x

• The number of quarters is half the number of nickels: x/2

2) He has 7 fewer dimes than nickels.

• That is: x - 7

3) Mulitiply each number of coins by its value in dollars:

• Dimes: (x - 7) × 0.10 = 0.10 (x - 7)

• Nickles: x × (0.05) = 0.05x

• Quarters: x/2 × 0.25 = 0.25×  (1/2 × x) = 0.25 (0.5x)

4) Add he values of all the coins:

• 0.10 (x - 7) + 0.05x + 0.25x

5) Equal to the total value of $ 5.90:

• 0.10 (x - 7) + 0.05x + 0.25x = 5.90

6) Compare with the equation written by Elliot:

• 0.10 (7 - x) + 0.5(x) + 0.25(0.5x)=5.90

7) Conclusion:

There are two errors:

• He wrote 7 - x, instead of 7 - x. That means that the first error was indicated by the first statement: He should have written the expression for the number of dimes as x - 7.

• He wrote 0.5x instead of 0.05x. That means that the second error was indicated by the third statement: He should have written the coin value for the nickel as 0.05.