Question

10.
11.

1. higher order thinking veronica wants to buy 1 3/4 pounds of cheese. when she checks some cheese in a container and weighs it, the scale shows 1 1/8 pounds. the container weighs 1/4 pound. how many more pounds of cheese should be added to the scale to get the amount that veronica needs? explain how you solved the problem.

be sure to find all of the questions you need to answer.

1. at a museum, jenny learned about a fossil that was three billion, four hundred million years old. write the fossil’s age in standard form and expanded form.
2. mixed with math four students raised $264 for a charity by washing cars. the students received $6 for each car they washed. how many cars did they wash?

Explanation:

Problem 12 (Veronica's Cheese Purchase)

Step 1: Find the weight of the cheese currently

The total weight (cheese + container) is $1\frac{1}{2}$ pounds, and the container weighs $\frac{1}{4}$ pound. To find the cheese weight, subtract the container weight from the total weight.
First, convert $1\frac{1}{2}$ to an improper fraction: $1\frac{1}{2}=\frac{3}{2}$.
Then, $\frac{3}{2}-\frac{1}{4}=\frac{6}{4}-\frac{1}{4}=\frac{5}{4}$ pounds of cheese currently.

Step 2: Find the additional cheese needed

Veronica needs $1\frac{3}{4}$ pounds of cheese. Convert $1\frac{3}{4}$ to an improper fraction: $1\frac{3}{4}=\frac{7}{4}$.
Subtract the current cheese weight from the needed weight: $\frac{7}{4}-\frac{5}{4}=\frac{2}{4}=\frac{1}{2}$ pound.

Step 1: Standard Form

"Three billion, four hundred million" is written as \( 3,400,000,000 \) in standard form (since 3 billion is \( 3 \times 10^9 \) and 400 million is \( 4 \times 10^8 \), so \( 3 \times 10^9 + 4 \times 10^8 = 3,400,000,000 \)).

Step 2: Expanded Form

Break down \( 3,400,000,000 \) by place value:
\( 3 \times 1,000,000,000 + 4 \times 100,000,000 + 0 \times 10,000,000 + 0 \times 1,000,000 + 0 \times 100,000 + 0 \times 10,000 + 0 \times 1,000 + 0 \times 100 + 0 \times 10 + 0 \times 1 \)
Simplified: \( 3 \times 10^9 + 4 \times 10^8 \) (or in full expanded form with all place values: \( 3,000,000,000 + 400,000,000 + 0 + 0 + 0 + 0 + 0 + 0 + 0 + 0 \)).

Step 1: Identify total money and cost per car

Total money raised: $264.
Cost per car washed: $8.

Step 2: Calculate number of cars

To find the number of cars, divide total money by cost per car: \( 264 \div 8 = 33 \).

Answer:

$\frac{1}{2}$ pound of cheese should be added.

Problem 13 (Fossil Age in Standard and Expanded Form)