Question

working with proportion
when given a ratio and one of the parts, write a proportion to solve using cross multiply and divide. use a letter or english words in the set - up to represent the parts to put the numbers in the correct location.
example 1: for a painting, greg mixes inks to get the tint he wants. he uses a ratio of yellow ink to white ink of 3:1. how many ml of yellow ink would he use if he used 500 ml of white ink?
solution: set up a proportion using the known ratio and english letters/words to represent the colours. the words are essential components of the proportion.
\\(\frac{yellow}{white}\\) \\(\frac{3}{1}=\frac{x}{500}\\)
\\(x = 3\times500\div1 = 1500\\) ml of yellow ink
example 2: for a painting, greg mixes inks to get the tint he wants. he uses a ratio of red ink to yellow in of 2:3. how many ml of yellow ink would he need if he used 500 ml of red ink?
solution: set up a proportion using the known ratio and english letters/words to represent the colours.
\\(\frac{red}{yellow}\\) \\(\frac{2}{3}=\frac{500}{x}\\)
\\(x = 3\times500\div2 = 750\\) ml of yellow ink
assignment 4 - working with proportion

1. if a secretary types 55 words in one minute, how long will it take the secretary to type a 2000 word report?

\\(\frac{words}{minutes}\\) \\(\frac{55}{1}\\)

1. the ratio between sams height and jesses height is 5:6. if jesse is 145 cm tall, how tall is sam? round your answer to the nearest whole centimeter.
2. a mechanic can rotate the 4 tires on a truck in 15 minutes. how many minutes would it take the mechanic to rotate the tires on 5 trucks? hint: what are you comparing??

Explanation:

Step1: Set up word-minute proportion

Let $x$ = time in minutes.
$\frac{\text{words}}{\text{minutes}} = \frac{55}{1} = \frac{2000}{x}$

Step2: Cross-multiply to solve for x

$55x = 2000 \times 1$
$x = \frac{2000}{55}$

Step3: Calculate the value of x

$x \approx 36.36$

Step1: Set up height ratio proportion

Let $x$ = Sam's height.
$\frac{\text{Sam's height}}{\text{Jesse's height}} = \frac{5}{6} = \frac{x}{145}$

Step2: Cross-multiply to solve for x

$6x = 5 \times 145$
$6x = 725$
$x = \frac{725}{6}$

Step3: Round to nearest whole number

$x \approx 121$

Step1: Find time per truck

1 truck takes 15 minutes.

Step2: Calculate time for 5 trucks

$\text{Total time} = 15 \times 5$

Answer:

1. Approximately 36.36 minutes
2. 121 cm
3. 75 minutes