Question

A shop sells one pound bags of peanuts for $2 and three-pound bags of peanuts for $5. if 9 bags are purchased for a total cost of $36, how many three-pound bags were purchased?

Answer 1

6

Step-by-step Step-by-step explanation:

Let c represent three-pound bags and a represent one-pound bags.

Use a system of equations:

{9 = c + a

{36 = 5c + 2a

−⅕[36 = 5c + 2a]

{9 = c + a

{−7⅕ = −c - ⅖a >> New Equation

____________

1⅘ = ⅗a

__ ___

⅗ ⅗

`3 = a` [Plug this back into both equations above to get the c-term of 6];
`6 = c`

I am joyous to assist you anytime.

Answer 2

1 bag = $2
3 bags = $5
9 bags = $36

we know someone unknown number of bags were sold
i'll represent those with a and b
a = number of 1 pound bags
b = number of 3 pound bags

2a + 5b = 36 ----- amount of money -(1)
a + b = 9 ------number of bags -(2)

from the second equation we have:
a = 9 - b
b = 9 - a

I'll use substitution method:
you could substitute either a or b into the equation (2)
I'll just use a

2a + 5b = 36
a = 9 - b

2(9 - b) + 5b = 36
18 - 2b + 5b = 36
-2b + 5b = 36 - 18
3b = 18
b = 6

no we know b = 6
we and to find a, we know that a = 9 - b
therefore a = 9 - 6
a = 3

the question only asked for the number of three pounds
which is represented here by b

therefore the answer of 3 pound bags is 6