In a recent year, a letter to europe from the united states costs $0.94 to mail. a letter mailed within the united states costs $0.44. nancy mailed 5 letters for $3.70, some to europe and some to the united states. how many letters did she send to europe

3 to Europe

Step-by-step explanation:

Let x represent the number of letters sent to Europe and y represent the number of letters sent to the U.S.

$0.94 for each letter sent to Europe gives us the expression 0.94x.

$0.44 for each letters sent to the U.S. gives us the expression 0.44y.

Together the total was $3.70; this gives us the equation

0.94x+0.44y = 3.70

There were 5 total letters sent; this gives us the equation

x+y = 5

This gives us the system

We will use substitution to solve this; we will isolate the variable x in the second equation.  We can do this by subtracting y from each side:

x+y = 5

x+y-y = 5-y

x=5-y

Next we substitute this into the first equation:

0.94x+0.44y = 3.70

0.94(5-y)+0.44y = 3.70

Using the distributive property,

0.94(5)-0.94(y)+0.44y = 3.70

4.7-0.94y+0.44y = 3.70

Combining like terms,

4.7-0.5y = 3.70

Subtract 4.7 from each side:

4.7-0.5y-4.7 = 3.7-4.7

-0.5y = -1

Divide both sides by -0.5:

-0.5y/-0.5 = -1/-0.5

y = 2

There were 2 letters mailed to the U.S.

Substitute this into the second equation:

x+2 = 5

Subtract 2 from each side:

x+2-2 = 5-2

x = 3

There were 3 letters mailed to Europe.

a) y = -3x +2

b) y = 1/2x -6

these 2 can be combined into one equation.

-3x +2 = .5x -6

8 = 3.5x

x = 8 / 3.5 = 2.2857142857

y = -3 * (8 / 3.5) +2

y = (-24 / 3.5) + 2

y = -4.8571428571

step-by-step explanation:

answer: first option i.e. 'a' is correct.

step-by-step explanation:

since we have given that

number of minutes to wrap a small gift box = 4 minutes

we need to find the number of gifts to be wrapped in 5 minutes

since there is a direct variation, as the number of minutes will increase with   number of gifts to be wrapped.

so, let the number of gifts to be wrapped in 5 minutes be x.

so, it becomes,

hence, first option 'a'   is correct.