Question

1. joel is $2\frac{1}{2}$ inches shorter than carlos. carlos is $1\frac{1}{4}$ inches taller than dan. if dan is $58\frac{1}{4}$ inches tall, how many inches tall is joel? 11. suzy spent $6\frac{1}{3}$ days working on her english project, $3\frac{1}{6}$ days doing her science project, and $1\frac{1}{2}$ days studying for her math test. how many more days did suzy spend on her english project and math test combined than on her science project? 12. higher order thinking veronica needs to buy $1\frac{3}{4}$ pounds of cheese. when the clerk places some cheese in a container and weighs it, the scale shows $1\frac{1}{4}$ pounds. the container weighs $\frac{1}{16}$ 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. 13. 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. 14. model with math four students raised money for a charity by washing cars. they received $15 for each car washed. how many cars...

Explanation:

Problem 10:

Step 1: Find Carlos's height

Dan's height is $58\frac{1}{4}$ inches. Carlos is $1\frac{1}{4}$ inches taller than Dan. So, Carlos's height = $58\frac{1}{4}+1\frac{1}{4}$.
Convert mixed numbers to improper fractions: $58\frac{1}{4}=\frac{58\times4 + 1}{4}=\frac{233}{4}$, $1\frac{1}{4}=\frac{5}{4}$.
Add them: $\frac{233}{4}+\frac{5}{4}=\frac{238}{4}=59\frac{2}{4}=59\frac{1}{2}$ inches.

Step 2: Find Joel's height

Joel is $2\frac{1}{2}$ inches shorter than Carlos. So, Joel's height = $59\frac{1}{2}-2\frac{1}{2}$.
Subtract the whole numbers and the fractions: $(59 - 2)+(\frac{1}{2}-\frac{1}{2}) = 57+0 = 57$ inches.

Step 1: Find the weight of the cheese alone

The scale shows $1\frac{1}{4}$ pounds (cheese + container), and the container weighs $\frac{1}{16}$ pound. So, cheese weight = $1\frac{1}{4}-\frac{1}{16}$.
Convert $1\frac{1}{4}$ to sixteenths: $1\frac{1}{4}=\frac{5}{4}=\frac{20}{16}$.
Subtract: $\frac{20}{16}-\frac{1}{16}=\frac{19}{16}=1\frac{3}{16}$ pounds.

Step 2: Find the amount of cheese to add

Veronica needs $1\frac{3}{4}$ pounds of cheese. Convert $1\frac{3}{4}$ to sixteenths: $1\frac{3}{4}=\frac{7}{4}=\frac{28}{16}$.
Cheese already present is $1\frac{3}{16}=\frac{19}{16}$ pounds.
Amount to add = $\frac{28}{16}-\frac{19}{16}=\frac{9}{16}$ pounds.

Step 1: Standard form

Three billion, four hundred million.

• Billion place: 3, Million place: 400, rest (thousands, ones) are 0.

So, standard form: $3,400,000,000$.

Step 2: Expanded form

Expanded form is the sum of each digit multiplied by its place value.
$3,400,000,000 = 3\times1,000,000,000+4\times100,000,000+0\times10,000,000+0\times1,000,000+0\times100,000+0\times10,000+0\times1,000+0\times100+0\times10+0\times1$
Simplify: $3\times10^9 + 4\times10^8$.

Answer:

Joel is $\boldsymbol{57}$ inches tall.

Problem 12: