Lesson Example Discussion Quiz: Class Homework |
Step-3 |
Title: Averages |
Grade: 8-a Lesson: S3-L1 |
Explanation: Let us verify the answer here with the steps. |
Description:
| Step | Type | Explanation | Answer |
|---|---|---|---|
1 |
Problem |
Jack’s average score in the last 8 tests is 70. What should be his score in his next test, so that his average score will be 72? |
|
2 |
Hint |
Formula used |
\$"Average" = "sum of set of numbers" / "amount of numbers in set"\$ |
3 |
Step |
The average score of 8 tests |
70 |
4 |
Step |
According to the formula |
\$("Sum of scores in 8 tests")/8 \$ = 70 |
5 |
Step |
Multiply both sides by 8 |
\$\cancel8^1 \times (8 "tests")/\cancel8^1 = 70 \times 8\$ |
6 |
Step |
Sum of scores in 8 tests |
560 |
7 |
Step |
Let \$x\$ be his score in his next test. |
|
8 |
Step |
Average score of 9 tests |
72 |
9 |
Step |
According to the formula |
\$("Sum of scores in 8 tests" + x)/9 \$ = 72 |
10 |
Step |
On simplification |
\$(560 + x)/9 \$ = 72 |
11 |
Step |
Multiply both sides by 9 |
\$\cancel9^1 \times (560 + x)/\cancel9^1 = 72 \times 9\$ ⇒ \$560 + x = 648\$ |
12 |
Step |
Subtract 560 from both sides. |
\$\cancel560 + x - \cancel560 = 648 - 560\$ ⇒ \$x = 88\$ |
13 |
Step |
So, Jack score in the next test should be |
88 |
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