Tony asked his friend to guess his mathematics test score. He gave these hints to help his friend guess:
-It has two digits
-The digit in the tens place is two more than twice the digit in the ones place.
-The number formed by reversing the order of the digits is 5 more than 3 times the sum of the digits.
What was his test score?
Answer is 83, but i'm not sure how it is worked out.
To determine Tony's mathematics test score, let's break down the hints given and solve the problem step by step:
Hint 1: It has two digits.
This means the score is any number between 10 and 99.
Hint 2: The digit in the tens place is two more than twice the digit in the ones place.
Let's use variables to represent the digits. Let's say the digit in the ones place is x. Therefore, the digit in the tens place would be 2x + 2.
Hint 3: The number formed by reversing the order of the digits is 5 more than 3 times the sum of the digits.
To reverse the order of the digits, we can multiply the digit in the ones place by 10 and add the digit in the tens place. So the reversed number is 10x + (2x + 2).
Now, we can set up an equation: 3 * (x + (2x + 2)) + 5 = 10x + (2x + 2).
Let's solve the equation step by step:
3 * (x + 2x + 2) + 5 = 10x + 2x + 2
3 * (3x + 2) + 5 = 12x + 2
9x + 6 + 5 = 12x + 2
9x + 11 = 12x + 2
11 - 2 = 12x - 9x
9 = 3x
x = 3
Since x represents the digit in the ones place, x = 3. Therefore, the digit in the tens place would be 2x + 2 = 2 * 3 + 2 = 8.
So the final answer is 83, which represents Tony's mathematics test score.
-It has two digits
_ _
-The digit in the tens place is two more than twice the digit in the ones place.
41 or 62 or 83
-The number formed by reversing the order of the digits is 5 more than 3 times the sum of the digits.
just write the words as math. If the tens digit is t and the units digit is u, then:
t = 2u+2
10u+t = 5+3(t+u)
solve for t and u