Question
Solve for the unknown number in the following expressions. a. \( y \div 3=4 R 2 \) b. \( 33 \div x=4 R 5 \) a. \( y=\square \)
Ask by Bowen Mccarthy. in the United States
Feb 27,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
a. \( y = 14 \)
b. \( x = 7 \)
Solution
To solve these problems, we use the division algorithm. When a number A is divided by B, the result is expressed as a quotient Q with remainder R, meaning:
A = B × Q + R
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Problem a: y ÷ 3 = 4 R 2
Here, A = y, B = 3, Q = 4, and R = 2. Plugging into the formula:
y = 3 × 4 + 2
y = 12 + 2
y = 14
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Problem b: 33 ÷ x = 4 R 5
Here, A = 33, B = x, Q = 4, and R = 5. Using the formula:
33 = x × 4 + 5
Subtract 5 from both sides:
33 - 5 = 4x
28 = 4x
Now, divide both sides by 4:
x = 28 ÷ 4
x = 7
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Final Answers:
a. y = 14
b. x = 7
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Simplify this solution Mind Expander
To solve for \( y \) in the expression \( y \div 3 = 4 R 2 \), we first interpret \( 4 R 2 \) as 4 with a remainder of 2. This means that when we divide \( y \) by 3, we get 4 as a quotient, and the leftover is 2. Therefore, we can write this as: \[ y = 3 \times 4 + 2 \] \[ y = 12 + 2 \] \[ y = 14 \] So, \( y = 14 \). Now, for \( x \) in \( 33 \div x = 4 R 5 \), we see that 4 R 5 means when we divide 33 by \( x \), we get a quotient of 4 and a remainder of 5. We can express that mathematically as: \[ 33 = 4x + 5 \] Subtracting 5 from both sides, we have: \[ 28 = 4x \] Now dividing both sides by 4 gives us: \[ x = 7 \] So, the solutions are: a. \( y = 14 \) b. \( x = 7 \)
