The triangles below are similar. Pls help me
2 answers:
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Answer:
Ernest gets 194 monthly allowance
Step-by-step explanation:
* Lets revise the rule of the average
- Average = The sum ÷ the total number
- Assume that the allowances money of Ernest, Jack, David and Mike
are E, J, D, M respectively
∵ The average allowance money of Ernest jack David and mike is
123 per month per person
∴ 123 = (E + J + D + M) ÷ 4
- Multiply both sides by 4
∴ E + J + D + M = 492 ⇒ (1)
∵ The average allowance of Ernest jack and David is 159 per month
per person
∴ 159 = (E + J + D) ÷ 3
- Multiply both sides by 3
∴ E + J + D = 477 ⇒ (2)
- Subtract equation(2) from equation (1) to find M
∴ M = 15
* <em>Mike's monthly allowance is 15</em>
∵ David's monthly allowance is 2 less than mikes
∴ D = M - 2
∵ M = 15
∴ D = 15 - 2 = 13
∴ <em>David's monthly allowance is 13</em>
∵ Mikes monthly allowance is 1/18 of jacks
∴ M = × J
∴ 15 = × J
- Multiply both sides by 18
∴ J = 270
* <em>Jack's monthly allowance is 270</em>
- Substitute the values of D , J in equation (2) to find E
∵ D = 13 and J = 270
∵ E + J + D = 477
∴ E + 270 + 13 = 477
∴ E + 283 = 477
- Subtract 283 from both sides
∴ E = 194
* <em>Ernest's monthly allowance is 194</em>
*<em> Ernest gets 194 monthly allowance</em>