Question

jenny is comparing the cost of two packages for socks 1 packages has eight pairs of socks for $12 another packages has three pairs of socks for $6 are the rates equivalent

Answer 1

Think about it like this. The rate is how much bang you're getting for your buck. In other words, how many pairs of socks are you getting for a given amount of money. 

Lets say I'm spending 12 dollars.

The first plan gives me 8 pairs. It's charging me 12/8 = 1.5 dollars for each pair of socks.

The second plan gives me 6 pairs. (3 pairs for 6 dollars, so if you double it then you get 6 pairs for 12 dollars). It's charging me 12/6 = 2 dollars for each pair of socks.

Since 2 > 1.5, I can say Plan 2 has a higher rate than Plan 1.

Answer 2

The rate for pair of socks can be calculated by dividing the packages of socks to the total cost of the socks.

The socks rate are not equal.

Given:

Cost for the 8 pairs of socks is $12 \:$.

Cost for the 3 pairs of socks is $6\:$.

Calculate the cost for the 1 pair of sock for first packages.

$\rm {Cost\: for\: the\: 1\: pair\: sock}=\frac{x}{y}$

Where,

$x$ is total pair of socks

$y$ is total cost.

$\begin{aligned}\rm {Cost\: for\: the\: 1\: pair\: sock}=\frac{8}{12}\\=0.67\:\\\\end$

Calculate the cost for the 1 pair of sock for second packages.

$\rm {Cost\: for\: the\: 1\: pair\: sock}=\frac{x}{y}$

Where,

$x$ is total pair of socks

$y$ is total cost.

$\begin{aligned}\rm {Cost\: for\: the\: 1\: pair\: sock}=\frac{3}{6} \\=0.60\:\\\end$

Thus, the rate for 1 pair of sock are different for each package.

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