The sum of 5 consecutive integers is 100. What is the first number in this sequence?
1 answer:
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Let's call:
a = price of 1 apple
p = price of 1 peach
The total cost is the price of 1 apple times the number of apples plus the price of 1 peach times the number of peaches, therefore the system can be:
Solve for a in the second equation (you can choose to solve for any of the variables in any of the equations, try to understand what is the best):
a = (4.82 - 5p) / 4
Now, substitute in the first equation:
6 · (4.82 - 5p) / 4 + 9p = 7.86
7.23 - (15/2)p + 9p = 7.86
(3/2)p = 0.63
p = 0.42
Now, substitute this value in the formula found for a:
<span>a = (4.82 - 5·0.42) / 4</span>
= 0.68
Therefore, one apple costs 0.68$ and one peach costs 0.42$.
a = price of 1 apple
p = price of 1 peach
The total cost is the price of 1 apple times the number of apples plus the price of 1 peach times the number of peaches, therefore the system can be:
Solve for a in the second equation (you can choose to solve for any of the variables in any of the equations, try to understand what is the best):
a = (4.82 - 5p) / 4
Now, substitute in the first equation:
6 · (4.82 - 5p) / 4 + 9p = 7.86
7.23 - (15/2)p + 9p = 7.86
(3/2)p = 0.63
p = 0.42
Now, substitute this value in the formula found for a:
<span>a = (4.82 - 5·0.42) / 4</span>
= 0.68
Therefore, one apple costs 0.68$ and one peach costs 0.42$.