Work out the value of [tex]$q$[/tex] when [tex]$q=\frac{3 r}{4}+1$[/tex] and [tex]$r=8$[/tex]
Answer (2)
The value of q is found to be 7 after substituting r = 8 into the equation q = 4 3 r + 1 and simplifying the expression. This involves multiplying, dividing, and then adding the numbers together. The final result shows that q = 7 .
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Substitute the given value of r into the equation.
Simplify the expression by performing the multiplication and division.
Add the remaining numbers to find the value of q .
The value of q is 7 .
Explanation
Understanding the Problem We are given the equation q = 4 3 r + 1 and the value r = 8 . Our goal is to find the value of q by substituting the given value of r into the equation.
Substitution Substitute r = 8 into the equation: q = 4 3 ( 8 ) + 1
Simplifying the Fraction Now, we simplify the expression: q = 4 24 + 1
Performing Division Perform the division: q = 6 + 1
Finding the Value of q Finally, add the numbers: q = 7 Therefore, the value of q is 7.
Examples
Imagine you are baking a cake and the recipe calls for a certain amount of flour based on the number of eggs you use. If the recipe states that the amount of flour (q) is calculated by multiplying the number of eggs (r) by 4 3 and then adding 1, and you are using 8 eggs, you can use this equation to determine the exact amount of flour you need. This ensures your cake turns out perfectly every time! This type of calculation is also useful in scaling recipes up or down.
