Question 1140371: A store is having a sale on jelly beans and trail mix. For 6 pounds of jelly beans and 2 pounds of trail mix, the total cost is $24. For 3 pounds of jelly beans and 5 pounds of trail mix, the total cost is $21. Find the cost of each pound of jelly beans and each pound of trail mix.
Found 2 solutions by josgarithmetic, ikleyn:
Answer by josgarithmetic(39617)   (Show Source):
Answer by ikleyn(52781)  (Show Source):
You can put this solution on YOUR website! .
From the condition, you have these two equations
6x + 2y = 24 (1)
3x + 5y = 21 (2)
where x is the price for 1 pound of jelly beans and y is the price for 1 pound of trail mix.
In equation (1), divide both sides by 2. Keep equation (2) as is.
3x + y = 12 (1')
3x + 5y = 21 (2')
Now subtract equation (1') from equation (2'). You will get
5y - y = 21 - 9
4y = 12
y = 12/4 = 3.
So, 3 dollars is the price for 1 pound of trail mix.
To find x, substitute y= 2 into equation (2). You will get
3x + 5*3 = 21, or 3x = 21 - 15 = 6 ====> y = 6/3 = 2.
ANSWER. $2 for one pound of jelly beans and $3 for one pound of trail mix.
Solved.
On the way, I applied the Elimination method to solve the system of 2 equations in 2 unknowns,
so now you know how it works.
|
|
|
