Grades 9-10 Video Solutions 2022-2022_9-10

Video Transcription

Question 5. A square of numbers is taken out from a multiplication table. Only one number is visible.  The integer x and y are both positive and x is greater than y. What is the value of x?  To solve this, we will take the sum of y and 1 and multiply it by the sum of x and 1 and set it equal to 77. To do this, we must do y times x giving us xy, y times 1,  we will add y times 1, then we will add 1 times x, and finally we will add 1 times 1.  This simplified gives us xy plus y plus x plus 1 equal to 77.  We can subtract 1 from both sides and now we can start inputting possible solutions.  We can start off with 6. Get 6y plus y plus 6 equal to 76. We can subtract 6 from both sides  and combine the y's, getting 7y equal to 70. Dividing both sides by 7, we get y equal to 10.  However, we have to keep in mind that x must be greater than y.  And since 6 is not greater than 10, we must cross this off. Next, we will try 7. 7y plus y plus 7  equal to 76. We get 8y equal to 69. We get y equals approximately 8.5. However, both the values  have to be integers. Since this has a decimal point, this is not an acceptable answer. As well,  it is still larger than x, so we can cross this off. Next, we try 8. We get 9y equal to 68,  or y approximately 7.5. Again, this is not an integer, so this cannot be the solution,  even though x is greater than y this time. Now, if we input 10, 10y plus y plus 10 equal to 76. Simplify down to 11y equals 66, or y equals 6. Both values are positive integers,  and x is greater than y, so the answer is D, 10.

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