Question

Please Geniuses, look at the picture and answer me, RESCUE ME.

Q1. if A:B= 6:5 and B:C= 18:6, then find A:C in its simplest term

A. 18:15
B. 15:18
C. 6:5
D. 5:6
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Answer 1

1.
`\{ \bold{ \sf{Expenditure \: on \: food = \:1200 dollars\: }}`

2.
`\sf{a \: : \: c \: = 18 \: : \: 5}`

Explanation:

1.
`\sf{here \: total \: expenditure = 3000 \: dollars}`

`\sf{expenditure \: on \: food \: = \: (3000)/(360) * 144}`

`\sf{expenditure \: on \: food{ = 1200 \: dollars}}`

Note : Whole circle represents the total expenditure.

i.e 360° represents $ 3000

1° represents $
`\sf{ (3000)/(360) }`

144 ° represents $
`\sf{ (3000)/(360) * 144}`

-------------------------------------------------------------

2.
`\sf{here \: a:b \: = 6:5 \: = \: (6)/(5) }`

`\sf{b : \: c \ \: = 18 \: : \: 6} \: = \: (18)/(6)`

`\sf{now \: a:b * b:c = (a)/(b) * (b)/(c) = (a)/(c) }`

⇒
`\sf{a:c = (6)/(5) * (18)/(6) }`

⇒
`\sf{a:c = (18)/(5) }`

⇒
`\sf{a:c = 18:5}`

Hope I helped!

Best regards!!