Luis goes to the store and buy three cans of juice and seven chocolates for $50. Eduardo bought two cans and six chocolates for $36. What is the price of each product?
Answer: price of juice cans = $12 ; price of chocolates = $2✔️
Explanation:
From the information they provide us, we have to establish the necessary equations to solve the problem.
Let x be the price of juice cans and y be the price of chocolates.
Luis purchased three cans of juice and seven chocolates for $50:
3x + 7y = $50 } Equation 1
Eduardo bought two cans and six chocolates for $36:
2x + 6y = $36 } Equation 2
We take the value of x from equation 1 and substitute it into equation 2:
x = ($50 - 7y)/3 } Equation 1
2x + 6y = $36 } Equation 2
2($50 - 7y)/3 + 6y = $36
2($50 - 7y)/3 + 6y = $36
2($50 - 7y) + 3*6y = 3*$36
$100 - 14y + 18y = $108
4y = $108 - $100
4y = $8
y = $8/4 = $2 , price of chocolates
x = ($50 - 7y)/3
x = ($50 - 7*$2)/3
x = ($50 - $14)/3
x = $36/3 = $12 , price of juice cans
Answer: price of juice cans = $12 ; chocolates = $2✔️.
Checking:
We can substitute these values in the equations:
3x + 7y = $50 } Equation 1
3*$12 + 7*$2 = $50
$36 + $14 = $50
$50 = $50✔️checked!
2x + 6y = $36 } Equation 2
2*$12 + 6*$2 = $36
$24 + $12 = $36
$36 = $36✔️checked!
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