mandy can buy 4 container of yogurt and 3 boxes of crackers for $9.55. she can buy 2 containers of yogurt and 2 boxes of crackers for $5.90. How much does one box of crackers cost?

Question

Answer: $2.25

Equations 4x + 3y = $9.55
2x + 2y = $5.90

Can anyone just help me with how to set the problem up, I can't figure out how to use the information given. Thanks

Answer 1

4 x + 3 y = 9.55 now multiply your second equation by 2
4 x + 4 y = 11.80

subtract the first equation from the second
0 x + 1 y = 11.80-9.55 = 2.25
the end

Answer 2

alternative to that which is called "elimination" is "substitution"
from the second equation
x + y = 5.90/2 = 2.95
so you can say
x = 2.95-y

now use that in the first equation
4(2.95-y) + 3 y = 9.55

11.80 - 4y + 3 y = 9.55
y = 11.80 -9.55 = 2.25 again

Answer 3

Thank you Damon

Answer 4

Why am I multiplying the second equation by 2?

Answer 5

Because there are two equations, perhaps?

Answer 6

don't understand where the 4x +4y = 11.80 come from with this ?

Answer 7

The 4x + 4y=11.80 comes from multiplying all the numbers by 2. But I did have the same question on why am I multiplying the second equation by 2 and my assumption is to cancel out x because we are only looking for the price of the crackers

Answer 8

The 4x + 4y=11.80 comes from multiplying all the numbers by 2. But I did have the same question on why am I multiplying the second equation by -2 and my assumption is to cancel out x because we are only looking for the price of the crackers

Answer 9

Hey Sunday,
A quick and simple trick i learned when i was still in grade school was.
4 yogurts and 3 boxes of crackers equals 9.55 dollars
2 yogurts and 2 boxes of crackers equals 5.90 dollars
you want to look at the difference between the yogurts since you need the individual price of one box of crackers. the first bit of information given is 4 yogurts and 3 boxes of crackers equals 9.55 dollars. in this information you notice that you have 2 more yogurts than the second bit of information 2 yogurts and 2 boxes of crackers equals 5.90 dollars. since the yogurts were divided by 2 you want to multiply the final price of the second line of information by 2.
5.90*2= 11.8
now subtract 11.8 from 9.55 and you get your answer of 2.25.

Answer 10

4x + 3y = 9.55
2x + 2y = 5.90
-2(2x + 2y) = -2(5.90)
*what you do to one side do to the other
-4x -4y = -11.80
4x + 3y = 9.55 (x’s cancel)
– y = -2.25
-y (-1)
Y = 2.25

Answer 11

I get it, first you want to set up the problem 4x + 3y = $9.55 then 2x = 2y multiply by 2 x $5.90 = 11.80 then subtract $9.55 from $11.80 = 2.25 this is the way I understand this math problem very helpful thank you.

Answer 12

I found it more easier this way: (elimination and substitution method)
Let y= yogurt
c= crackers
First: solve for y
4y + 3c = 9.55 2y + 2c = 5.90 (divide both side by 2)
4 (2.95-c) + 3c= 9.55 y + c = 2.95 (subtract by c)
11.80 - 4c +3c = 9.55 y = 2.95 - c (substitute to first equation)
-11.80 = 11.80
-1c. = -2.25 (divide both sides by -1)
c = 2.25

Check: 4 (2.95- 2.25)+ 3 (2.25) = 9.55
4 (0.70) + 6.75 = 9.55
2.80 + 6.75 = 9.55
9.55 = 9.55

The answer is $2.25 for a box of crackers .

Answer 13

Forgot that it doesn't automatically indent the text on how I want them to. Here is the better (non-confusing) way to solve it:

Equations:
4y + 3c = $9.55
2y + 2c = $ 5.90

First: solve for Y
(using 2nd equation)
2y + 2c = 5.90 (divide both sides by 2)
y + c = 2.95 (subtract by c)
y = 2.95-c (substitute y of 1st equation)

Second: solve 1st equation using Y substitution.
4y + 3c =$9.55
4 (2.95-c) + 3c = 9.55
11.80- 4c + 3c = 9.55
-11.80 = 11.80
-1c= -2.25 (divide both sides by -1)
c= 2.25

The answer is $2.25 for a box of crackers.