MATH SOLVE

4 months ago

Q:
# 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?

Accepted Solution

A:

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

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