Final answer:
To solve for variables in each proportion, cross-multiplication is used. Solutions are found by multiplying the means and extremes and then dividing by the coefficient of the variable, yielding E = 2, T = 6, L = 27, W = 15, and I = 1.8.
Step-by-step explanation:
To solve for variables in each proportion, we use the property of cross-multiplication. For the first equation, E/5 = 14/35, we cross-multiply to get 35E = 5 × 14, which simplifies to 35E = 70. Dividing both sides by 35 gives E = 70/35, resulting in E = 2.
For 7/28 = T/24, cross-multiplication yields 28T = 7 × 24, which simplifies to 28T = 168. Dividing both sides by 28 gives T = 168/28, resulting in T = 6.
In the third proportion, given by 9/10 = L/30, cross-multiplication leads to 10L = 9 × 30, which simplifies to 10L = 270. Dividing both sides by 10 gives L = 270/10, resulting in L = 27.
The proportion 20/30 = 10/W simplifies to 2/3 = 10/W. Cross-multiplication gives 2W = 3 × 10, which results in 2W = 30. Dividing by 2, we get W = 30/2, leading to W = 15.
In the next proportion, 12/20 = 3/I, the process of cross-multiplication gives us 20I = 12 × 3, which simplifies to 20I = 36. Dividing by 20, we find I = 36/20, which simplifies to I = 9/5 or I = 1.8.