Last Sunday, the average temperature was $8 \%$ higher than the average temperature two Sundays ago. The average temperature two Sundays ago was $T$ degrees Celsius. $\newline$ Which of the following expressions could represent the average temperature last Sunday? $\newline$ Choose $2$ answers: $\newline$ A) $1.08 T$ $\newline$ B) $T+0.08$ $\newline$ C) $T+8$ $\newline$ D) $\left(1+\frac{8}{100}\right) T$ $\newline$ E) $1.8 T$

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Grade 8

Identify equivalent linear expressions: word problems

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Q. Last Sunday, the average temperature was

8 \%

higher than the average temperature two Sundays ago. The average temperature two Sundays ago was

T

degrees Celsius.

\newline

Which of the following expressions could represent the average temperature last Sunday?

\newline

Choose

2

answers:

\newline

1.08 T

\newline

T+0.08

\newline

T+8

\newline

\left(1+\frac{8}{100}\right) T

\newline

1.8 T

Calculate $8\%$ Increase: To find the average temperature last Sunday, which was $8\%$ higher than the average temperature two Sundays ago, we need to increase the temperature from two Sundays ago by $8\%$ . The temperature two Sundays ago is given as $T$ degrees Celsius.
Convert Percentage to Decimal: An $8\%$ increase can be calculated by multiplying the original amount by $1$ plus the percentage increase expressed as a decimal. To convert a percentage to a decimal, we divide by $100$ . Therefore, $8\%$ as a decimal is $\frac{8}{100}$ or $0.08$ .
Multiply Original Temperature: Now we multiply the original temperature $T$ by $1 + 0.08$ to find the new temperature. This gives us $T \times (1 + 0.08)$ which simplifies to $T \times 1.08$ .
Check Answer Choices: We can now check the answer choices to see which ones match our expression $T \times 1.08$ . Choice A is $1.08T$ , which matches our expression exactly.
Identify Correct Representations: Choice D is $(1 + (\frac{8}{100}))T$ , which simplifies to $(1 + 0.08)T$ , which is also $T \times 1.08$ . So, choice D is also a correct representation of the average temperature last Sunday.
Identify Correct Representations: Choice D is $(1 + (\frac{8}{100}))T$ , which simplifies to $(1 + 0.08)T$ , which is also $T \times 1.08$ . So, choice D is also a correct representation of the average temperature last Sunday.Choices B, C, and E do not correctly represent an $8\%$ increase. Choice B is $T + 0.08$ , which would only add $0.08$ degrees to $T$ , not $8\%$ . Choice C is $T + 8$ , which adds $8$ degrees to $T$ , not $8\%$ . Choice E is $(1 + 0.08)T$ $2$ , which would represent an $(1 + 0.08)T$ $3$ increase, not $8\%$ .