Question

Rachel paints 5 1 2 512 square meters of wall space in 1 3 13 hour. What area of wall space can she paint in 1 hour? One 200-gram bag of rice costs $8.12. How much does 1 kilogram of rice cost? (Note that 1000 g = 1 kg.) John ran 1 2 12 mile in 5 minutes, and Al ran 1 3 13 mile in 4 minutes. Which runner ran at a faster rate? At a certain store, a half-gallon jug of milk costs $2.95, and a gallon jug of milk costs $5.95. Which milk has a cheaper price: the half-gallon or gallon jug? A package of nine 12-ounce cans of cola costs $7.50. A half-gallon bottle of the same cola is sold for $2.90. Which cola has a cheaper price, the cans or the bottle?

Answer 1

QUESTION 1

It was given that Rachel can paint 512 square meters of wall in 13 hours.

We can write the ratio,

$512\:m^2:13\:h$.

We want to find what area of wall space she can paint in 1 hour.

Let the area of wall space she can paint in 1 hour be $x$ square meters.

We  can again write the ratio,

$x\:m^2:1\:h$.

We know this is going to be less, so if less more divides.

$x=\frac{1\times 512}{13} m^2$

This gives,

$x\approx 39.38m^2$ to the nearest hundredth.

QUESTION 2

It was given that;

$200g:8.12\:dollars$.

We want to find how much one kilogram of rice costs and we also know that,

$1kg=1000g$.

so we let $x$ be the cost of 1 kg.

Then,

$1000g:x\:dollars$.

We know this is going to be more,so if more less divides,

$x=\frac{8.12\times 1000}{200}\:dollars$

$x=40.6\:dollars$

Therefore 1k cost $ 40.60

QUESTION 3

We were given that, John ran 12 miles in 5 minutes.

We can write this ratio as

$12:5$

or

$\frac{12}{5}$

Al ran 13 miles in  4 minutes.

We can write this one too as,

$13:4$ or

$\frac{13}{4}$

The least common denominator for the two fractions is 20.

In equivalent fractions, John 's rate is

$\frac{12}{5}=\frac{48}{20}$

and

Al's rate is

$\frac{13}{4}=\frac{65}{20}$

We can see that, in 20 minutes, John covers 48 miles while Al covers 65 miles.

Hence, Al ran at a faster rate.

QUESTION 4

We were given that, a half-gallon jug of milk costs $ 2.95 at a certain store.

We can write this as a ratio to get,

$\frac{1}{2}\:jug:2.95\:gallon$.

When we multiply each term of the ratio by 2, we get,

$1\:jug:5.90\:gallon$.

This means that 1 jug of milk costs $ 5.90 at this same store.

We were given that at another store, a gallon jug of milk costs $ 5.95.

Therefore the half gallon jug of milk for $ 2.95  is cheaper.

QUESTION 5

We were given that at a certain store, a package of nine 12-ounce cans of cola costs $7.50

Nine 12 ounce cans corresponds 108 ounces in total.

If 108 ounces corresponds to $ 7.50, then,

64 ounces corresponds to $\frac{64\times 7.50}{108}=4.44 \:dollars$.

This means that a half-gallon cola in this store costs approximately $ 4.44.

If a half- gallon bottle of the same cola is sold for 2.90 dollars at a different store, this one is cheaper.

Hence the bottle is cheaper.