Answered

Donald has $p$ amount of 20-dollar bills and 1 ten-dollar bill. Write an expression to show how to find how much money Donald has. How much money does he have if $p = 20$?

Verified Answer :

  • Define the expression for total money: \(T = 20p + 10\).
  • Substitute the value \(p = 20\) into the expression: \(T = 20(20) + 10\).
  • Calculate the total: \(T = 400 + 10 = 410\).
  • Final answer: \(\boxed{\$410}\).

Explanation

  1. Formulating the Expression for Total Money

To determine the total amount of money Donald has, we identify the components of his cash:

  1. He has \(p\) bills, each worth \(\$20\). The total value from these bills is given by the product of the number of bills and the value of each bill, which is \(20 \times p = 20p\).
  2. He has one \(\$10\) bill, which contributes \(\$10\) to the total.

The total amount of money, which we can call \(T\), is the sum of these two values:
\[T = 20p + 10\]

  1. Calculating Total Money for p = 20

We are asked to find the total amount of money when Donald has \(p = 20\) bills of \(\$20\).
Substituting \(p = 20\) into our expression for \(T\):
\[T = 20(20) + 10\]
Calculating the product:
\[20 \times 20 = 400\]
Adding the value of the \(\$10\) bill:
\[400 + 10 = 410\]
Thus, the total amount of money Donald has is \(\$410\).

Examples

Algebraic expressions help us model real-world scenarios, such as tracking expenses or savings. For instance, if you receive a fixed allowance of \(\$10\) and earn \(\$20\) for every hour (\(h\)) you mow lawns, your total weekly income can be represented by the expression \(20h + 10\). By substituting the number of hours you worked, you can easily calculate your total earnings for the week.

Related Questions