3 years ago

3 equivalent ratios of 6:7

Mathematics

1 answer:

LenaWriter [7]3 years ago

4 0

Answer:

3:3.5, 9:10.5, 12:14

Step-by-step explanation:

6:7 divided by 2 = 3:3.5

6:7 multiplied by 1.5 = 9:10.5

6:7 multiplied by 2 = 12:14

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$a_n=a_1+(n-1)d$

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$21=(n-1)d$

$n$ has to be an integer, which means there are 4 possible cases.

Case 1: $n-1=1$ and $d=21$ . But

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Case 2: $n-1=21$ and $d=1$ . But

$\displaystyle\sum_{k=1}^{22}(8+1(k-1))=407\neq123$

Case 3: $n-1=3$ and $d=7$ . But

$\displaystyle\sum_{k=1}^4(8+7(k-1))=74\neq123$

Case 4: $n-1=7$ and $d=3$ . But

$\displaystyle\sum_{k=1}^8(8+3(k-1))=148\neq123$

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