Math Problem Monday - October 17th, 2022 | Mathnasium Livermore, CA

Lower Elementary:
Question: John ate 17 grapes this week. He ate twice as many last week as he did this week. He ate twice as many two weeks ago as he did last week. How many grapes did John eat two weeks ago?
Answer: 68 grapes
Solution: John ate twice as many grapes last week as he did this week. 17 doubled = 10 doubled + 7 doubled = 20 + 14 = 34. John ate 34 grapes last week. He ate twice as many grapes two weeks ago as he did last week. 34 doubled = 30 doubled = 4 doubled = 60 + 8 = 68. John ate 68 grapes two weeks ago.

Upper Elementary:
Question: Julian spent a total of $690 on an annual pass for a theme park for a whole year. There was a $150 down payment. Then the remaining amount was divided evenly into monthly payments. How much were the monthly payments?
Answer: $45
Solution: First we need to find how much more Julian had to pay after paying the down payment. $690 – $150 = $540. Since there are 12 months in a year, we need to divide the amount without the down payment by 12 to see how much the monthly payments are. $540 ÷ 12 = $45. The monthly payments are $45.

Middle School:
Question: Ben’s bill was $20. The tax is 10%. He wants to leave a tip equal to 15% of the bill without tax. If he pays with a $35 gift card, how much money is left on the gift card?
Answer: $10
Solution: The amount for tax is 10% of $20 = $2. The amount for the tip is 15% of $20 = $3. So the entire bill is $20 + $2 + $3 = $25. Since the gift card was $35, the amount left on the gift card is $35 – $25 = $10.

Algebra and Up:
Question: The sum of three consecutive integers is 264. What are the integers?
Answer: 87, 88, and 89
Solution: Let n represent the smallest integer. Since the numbers are consecutive, the middle integer is n + 1 and the largest integer is n + 2. So, we have that n + (n + 1) + (n + 2) = 264.
Combine the like terms.
3n + 3 = 264
Subtract 3 from both sides.
3n = 261
Divide both sides by 3.
n = 87
The smallest integer is 87. Since the integers are consecutive, the other two numbers are 88 and 89. So, 87, 88, and 89 are the three consecutive integers that sum to 264.