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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?

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QUESTION 1

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


We can write the ratio,

[tex]512\:m^2:13\:h[/tex].

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 [tex]x[/tex] square meters.


We  can again write the ratio,


[tex]x\:m^2:1\:h[/tex].

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


[tex]x=\frac{1\times 512}{13} m^2[/tex]

This gives,

[tex]x\approx 39.38m^2[/tex] to the nearest hundredth.


QUESTION 2

It was given that;

[tex]200g:8.12\:dollars[/tex].

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

[tex]1kg=1000g[/tex].


so we let [tex]x[/tex] be the cost of 1 kg.


Then,

[tex]1000g:x\:dollars[/tex].


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

[tex]x=\frac{8.12\times 1000}{200}\:dollars[/tex]


[tex]x=40.6\:dollars[/tex]


Therefore 1k cost $ 40.60


QUESTION 3

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

We can write this ratio as

[tex]12:5[/tex]

or

[tex]\frac{12}{5}[/tex]

Al ran 13 miles in  4 minutes.


We can write this one too as,

[tex]13:4[/tex] or

[tex]\frac{13}{4}[/tex]


The least common denominator for the two fractions is 20.


In equivalent fractions, John 's rate is

[tex]\frac{12}{5}=\frac{48}{20}[/tex]


and

Al's rate is

[tex]\frac{13}{4}=\frac{65}{20}[/tex]


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,

[tex]\frac{1}{2}\:jug:2.95\:gallon[/tex].

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

[tex]1\:jug:5.90\:gallon[/tex].

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 [tex]\frac{64\times 7.50}{108}=4.44 \:dollars[/tex].

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.




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