1. What is the constant of proportionality?
2 answers:
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Answer:
$490
Step-by-step explanation:
Shauna spent $175 on a pair of shoes.
She spent 1/9 of the remaining money on a shirt.
If he still had 4/7 of his money left,how much did he have at first ?
Solution:
Let at first, Shauna have =
Money spent on a pair of shoes = $175
Remaining money =
<u>As she spent 1/9 of the remaining money on a shirt.</u>
Money spent on shirt =
As he still had of his money left:-
Money left =
Money left with Shauna = Total money, she had at first -(Money spent on a pair of shoes + Money spent on shirt )
Subtracting both sides by and adding both sides by
Taking LCM of 7 and 9, we get 63
Adding both side by -
By cross multiplication:
Dividing both sides by 180
Therefore, total $490, she had at first.
The sum of the first four terms of the sequence is 22.
In this question,
The formula of sum of linear sequence is
The sum of the first ten terms of a linear sequence is 145
⇒
⇒ 145 = 5 (2a+9d)
⇒
⇒ 29 = 2a + 9d ------- (1)
The sum of the next ten term is 445, so the sum of first twenty terms is
⇒ 145 + 445
⇒
⇒ 590 = 10 (2a + 19d)
⇒
⇒ 59 = 2a + 19d -------- (2)
Now subtract (2) from (1),
⇒ 30 = 10d
⇒ d =
⇒ d = 3
Substitute d in (1), we get
⇒ 29 = 2a + 9(3)
⇒ 29 = 2a + 27
⇒ 29 - 27 = 2a
⇒ 2 = 2a
⇒ a =
⇒ a = 1
Thus, sum of first four terms is
⇒
⇒
⇒ S₄ = 2(2+9)
⇒ S₄ = 2(11)
⇒ S₄ = 22.
Hence we can conclude that the sum of the first four terms of the sequence is 22.
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