What multiplies to 60 and adds to 19
The Correct Answer and Explanation is:
To solve the problem “What multiplies to 60 and adds to 19?”, we are looking for two numbers that satisfy both conditions:
- Their product is 60
- Their sum is 19
Step 1: Understand the question
We are given the product (60) and the sum (19). We need to find two numbers (let’s call them x and y) such that:
- x⋅y=60x \cdot y = 60x⋅y=60
- x+y=19x + y = 19x+y=19
Step 2: List all factor pairs of 60
We list pairs of numbers that multiply to 60:
- 1×601 \times 601×60
- 2×302 \times 302×30
- 3×203 \times 203×20
- 4×154 \times 154×15
- 5×125 \times 125×12
- 6×106 \times 106×10
Now check which pair adds to 19:
- 1+60=611 + 60 = 611+60=61
- 2+30=322 + 30 = 322+30=32
- 3+20=233 + 20 = 233+20=23
- 4+15=194 + 15 = 194+15=19 ✅
- 5+12=175 + 12 = 175+12=17
- 6+10=166 + 10 = 166+10=16
The pair 4 and 15 multiply to 60 and add up to 19.
Final Answer:
The two numbers are 4 and 15.
Textbook-style Explanation
In algebra and number sense, problems that ask for two numbers based on their sum and product are foundational to understanding factoring and quadratic equations. This type of problem often appears when factoring trinomials or solving real-life scenarios involving area and perimeter.
In this case, we are asked to determine two numbers whose product is 60 and whose sum is 19. To approach this, one effective method is to begin by identifying factor pairs of 60, since the product is a key clue. Factor pairs are sets of two numbers that, when multiplied together, yield the target product. The factor pairs of 60 are:
- (1, 60)
- (2, 30)
- (3, 20)
- (4, 15)
- (5, 12)
- (6, 10)
Once all factor pairs are identified, each pair is tested by calculating their sum to check whether it matches the given sum of 19. Among these pairs, the pair (4, 15) not only multiplies to 60 but also sums to 19, satisfying both conditions of the problem.
Thus, the answer is that the two numbers are 4 and 15. This problem illustrates a basic yet important concept in mathematics: understanding the relationship between multiplication and addition, which lays the groundwork for more advanced algebraic thinking and problem-solving.
