Ivan buys candy that costs $7 per pound. He will buy at most 9 pounds of candy. What are the possible amounts he will spend on c
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To eliminate all of the fractions in an equation, we can multiply the equation by the least common denominator of all of the fractions in the equation. To find the LCD, we need to find a number that has at least all of the factors of each of the denominators.
To find the LCD of the fractions in this equation, let's look at our denominators, 3 and 6. We can say 3 = 3 and 6 = 2 * 3. By examining this, we can see that our LCD <em>has to have </em>a 3 and 2, since those numbers are found in at least one of the fractions. Thus, our LCD is 3 * 2 = 6.
Now we know to multiply our entire equation by 6. This is solved as shown:
Our answer is 4x + 42 = 5.
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Let us translate the sentences to mathematics for ease!
A 3-digit number
Ones digit → ( let p represent is )
Hundreds digit is four more than ones digit → ( 4 + p )
Tens digit is twice hundreds digit → 2 ( 4 + p ) = 8 + 2p
Sum of the digits is 12
↓
Hundreds digit + Tens digit + Ones digit = 12
( 4 + p ) + ( 8 + 2p ) + p = 12
Combine like terms
4 + 8 + p + p + 2p = 12
12 + 4p = 12
Take 12 to the opposite side { Do subtraction when you see addition }
12 ( - 12 ) + 4p = 12 - 12
4p = 0
Divide by 4 on either side
p = 0
( 4 + 0 ) + ( 8 + 2 ( 0 ) ) + ( 0 )
The number is 480
Check
Hundreds + Tens + Ones = 12
4 + 8 + 0 = 12
12 = 12
Let us translate the sentences to mathematics for ease!
A 3-digit number
Ones digit → ( let p represent is )
Hundreds digit is four more than ones digit → ( 4 + p )
Tens digit is twice hundreds digit → 2 ( 4 + p ) = 8 + 2p
Sum of the digits is 12
↓
Hundreds digit + Tens digit + Ones digit = 12
( 4 + p ) + ( 8 + 2p ) + p = 12
Combine like terms
4 + 8 + p + p + 2p = 12
12 + 4p = 12
Take 12 to the opposite side { Do subtraction when you see addition }
12 ( - 12 ) + 4p = 12 - 12
4p = 0
Divide by 4 on either side
p = 0
( 4 + 0 ) + ( 8 + 2 ( 0 ) ) + ( 0 )
The number is 480
Check
Hundreds + Tens + Ones = 12
4 + 8 + 0 = 12
12 = 12