Question

mel3e – mathematics for everyday life
four: use common ratios (equivalent fractions) to find the estima
\\(\frac{19\\,\text{mm}}{5\\,\text{km}} = \frac{42\\,\text{mm}}{x\\,\text{km}}\\)
\\(\frac{19\\,\text{mm}}{5\\,\text{km}}\\) \\(\frac{42\\,\text{mm}}{x\\,\text{km}}\\) cross multiply
\\(19(x) = 5(42)\\)
\\(19x = 210\\)
\\(\frac{19x}{19} = \frac{210}{19}\\)
\\(x = \frac{210}{19}\\)
\\(x \approx 11.05\\,\text{km}\\)
therefore the distance between cannington and sunderland is 11.06 km.
support questions

1. find the value of \x\ for each situation set of ratios given below:

a. \\(\frac{5}{12} = \frac{x}{48}\\)
b. \\(\frac{3}{70} = \frac{x}{351}\\)
c. \\(\frac{8}{6} =\\)

Explanation:

Part a:

Step1: Cross - multiply the proportion

Given the proportion \(\frac{5}{12}=\frac{x}{48}\), cross - multiplying gives us \(12\times x = 5\times48\).

Step2: Simplify the right - hand side

Calculate \(5\times48 = 240\), so the equation becomes \(12x=240\).

Step3: Solve for x

Divide both sides of the equation \(12x = 240\) by 12. \(\frac{12x}{12}=\frac{240}{12}\), which simplifies to \(x = 20\).

Part b:

Step1: Cross - multiply the proportion

Given the proportion \(\frac{3}{70}=\frac{x}{351}\), cross - multiplying gives us \(70\times x=3\times351\).

Step2: Simplify the right - hand side

Calculate \(3\times351 = 1053\), so the equation becomes \(70x = 1053\).

Step3: Solve for x

Divide both sides of the equation \(70x = 1053\) by 70. \(x=\frac{1053}{70}\approx15.04\) (rounded to two decimal places)

Part a Answer: \(x = 20\)

Part b Answer: \(x=\frac{1053}{70}\approx15.04\) (if we consider the third part, since it is cut off, we can't solve it without complete information. But for the given a and b parts, the answers are as above)

Answer:

Step1: Cross - multiply the proportion

Given the proportion \(\frac{3}{70}=\frac{x}{351}\), cross - multiplying gives us \(70\times x=3\times351\).

Step2: Simplify the right - hand side

Calculate \(3\times351 = 1053\), so the equation becomes \(70x = 1053\).

Step3: Solve for x

Divide both sides of the equation \(70x = 1053\) by 70. \(x=\frac{1053}{70}\approx15.04\) (rounded to two decimal places)

Part a Answer: \(x = 20\)

Part b Answer: \(x=\frac{1053}{70}\approx15.04\) (if we consider the third part, since it is cut off, we can't solve it without complete information. But for the given a and b parts, the answers are as above)