problem # 1 No Zeroes
two numbers multiply to give 100 000. Neither of them contain a zero. What are the numbers?
problem # 2 Junk Food
a burger and a cola togerther cost $3.25.
If the burger costs $1.75 more than the cola, how much does the cola cost?
PLZ HELP FAST!!!!!!!!!!!!!!
ms.sue plz help me
32 x 3125 = 100000
#2
cola -- x
burger --- x+1.75
x + x +1.75 = 3.25
solve for x
thanx reiny i realyy appreciate t ill try and answer ur question
Problem #1: No Zeroes
To find the two numbers that multiply to give 100,000 and do not contain a zero, we can use a systematic approach.
1. Start by finding the prime factorization of 100,000: 100,000 = 2^5 * 5^5.
2. Notice that for both numbers to not contain a zero, they cannot have any factors of 10, which is 2 * 5.
3. Consider the factors of 100,000 that are powers of 2 and powers of 5. We have the options:
- 2^1 * 5^4 and 2^4 * 5^1
- 2^2 * 5^3 and 2^3 * 5^2
4. Calculate the values of these options:
- Option 1: (2^1 * 5^4) * (2^4 * 5^1) = 2^5 * 5^5 = 100,000 (contains zeros)
- Option 2: (2^2 * 5^3) * (2^3 * 5^2) = 2^5 * 5^5 = 100,000 (contains zeros)
5. None of the options work, meaning there are no two numbers that multiply to give 100,000 without containing a zero.
Therefore, there are no two numbers that meet the given conditions.
Problem #2: Junk Food
Let's assume the cost of the cola is x dollars. Since the burger costs $1.75 more than the cola, we can represent the cost of the burger as (x + $1.75).
According to the problem, the cost of the burger and the cola together is $3.25. The equation representing this is:
x + (x + $1.75) = $3.25
Simplifying the equation:
2x + $1.75 = $3.25
Subtracting $1.75 from both sides:
2x = $3.25 - $1.75
2x = $1.50
Dividing both sides by 2:
x = $1.50 / 2
x = $0.75
Therefore, the cost of the cola is $0.75.