Question

Write in complete sentences the procedure that you follow in solving the following problem:

An automatic teller machine gives you $150 in five and ten-dollar bills. There are two more than twice as many five-dollar bills as there are ten-dollar bills. How many of each denomination are there?
Step 1:
Step 2:
And so on…
Solve the problem completely and express your final answer in a complete sentence.

Answer 1

To determine the number of five and ten-dollar bills dispensed by the ATM totaling $150, create an equation based on the given relationship and solve for the variable representing the number of ten-dollar bills. The machine dispensed 7 ten-dollar bills and 16 five-dollar bills.

Step-by-step explanation:

To solve the problem of determining the number of five-dollar and ten-dollar bills dispensed by an automatic teller machine that gave out $150 in total, follow these steps:

1. Let the number of ten-dollar bills be x.
2. According to the given information, the number of five-dollar bills is twice the number of ten-dollar bills plus two, so it will be 2x + 2.
3. Set up the equation representing the total amount of money dispensed in terms of x: 10x + 5(2x + 2) = 150.
4. Simplify the equation: 10x + 10x + 10 = 150.
5. Combine like terms: 20x + 10 = 150.
6. Subtract 10 from both sides of the equation: 20x = 140.
7. Divide both sides by 20 to find the value of x: x = 7.
8. The number of ten-dollar bills is 7, and the number of five-dollar bills is 2(7) + 2 = 16.

Therefore, the automatic teller machine dispensed 7 ten-dollar bills and 16 five-dollar bills.