Chapter 3: Q. 379 (page 406)

Paulette has $$140$ in $$ 5$ and $$10$ bills. The number of $$ 10$ bills is one less than twice the number of $$ 5$ bills. How many of each does she have?

Short Answer

Expert verified

The number of $$ 10$ billsis $11$ and the number of $$ 5$ bills is $6 .$

Step by step solution

Step 1. Given Information

The number of $$ 10$ bills is one less than twice the number of $$ 5$ bills and Paulette has $$ 140$ in $$ 5 and $ 10$ bills. We have to find the number of each bill she has.

Step 2. Create a table

Let xbe the number of $$ 5$ bills.

Now, the number of $$ 10$ bills is one less than twice the number of $$ 5$ bills.

So, the number of $$ 10$ bills $= 2 x - 1$

Thus, the table is

Type	$Number \cdot Value ($) = Total Value ($)$
$$ 5$	$x$	$$ 5$	$5 (x)$
$$ 10$	$2 x - 1$	$$ 10$	$10 (2 x - 1)$

The total $$ 5 and $ 10 bills are $ 140 .$

Step 3. Translate into an equation

Write the equation by adding the total value of all the types of coins.

So, $5 (x) + 10 (2 x - 1) = 140$

Step 4. Solve the equation

By proceeding with the equation we get,

$5 (x) + 10 (2 x - 1) = 140 5 x + 20 x - 10 = 140 25 x = 150 x = \frac{150}{25} x = 6$

Thus, the number of bills of $$ 5 is 6$ and the number of bills of $$ 10 is [2 (6) - 1] = 11$ .

Step 5. Check the answer

To check the answer replace xby $6$ into the original equation.

$5 (6) + 10 [2 (6) - 1] = 140 30 + 10 [11] = 140 30 + 110 = 140 140 = 140$

It is true.

Thus, the number of

$ 5

bill is

6

and the number of

$ 10

bill is

11 .

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Paulette has $\(140$ in $\) 5$ and $\(10$ bills. The number of $\) 10$ bills is one less than twice the number of $$ 5$ bills. How many of each does she have?

Short Answer

Step by step solution

Step 1. Given Information

Step 2. Create a table

Step 3. Translate into an equation

Step 4. Solve the equation

Step 5. Check the answer

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Paulette has \(140 in \)5 and \(10 bills. The number of \)10 bills is one less than twice the number of $5 bills. How many of each does she have?

Short Answer

Step by step solution

Step 1. Given Information

Step 2. Create a table

Step 3. Translate into an equation

Step 4. Solve the equation

Step 5. Check the answer

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Statistics

Decision Maths

Logic and Functions

Calculus

Probability and Statistics

Theoretical and Mathematical Physics

Study anywhere. Anytime. Across all devices.

Paulette has $\(140$ in $\) 5$ and $\(10$ bills. The number of $\) 10$ bills is one less than twice the number of $$ 5$ bills. How many of each does she have?