Ggle is saying the wrong answer, anyone can help??
2 answers:
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Votes received by Wayne is 112
<em><u>Solution:</u></em>
To find: votes received by Wayne
Let the vote received by Wayne be "x"
<em><u>Juan received 4 times as many votes as Wayne</u></em>
Therefore,
Juan votes = 4 times as many votes as Wayne
Juan votes = 4x ---- eqn 1
<em><u>Neal received twenty less votes than Juan</u></em>
Neal votes = twenty less votes than Juan
Neal votes = Juan votes - 20
Neal votes = 4x - 20 ---- eqn 2
<em><u>Kerry got half as many votes as Neal</u></em>
Kerry votes = half of neal votes
Kerry votes = ---- eqn 3
The total votes cast in the election was 1,202
Wayne votes + Juan votes + Neal votes + Kerry votes = 1202
Plug in eqn 1 , eqn 2, eqn 3
Therefore votes received by Wayne is 112
Answer:
We can do it with envelopes with amounts $1,$2,$4,$8,$16,$32,$64,$128,$256 and $489
Step-by-step explanation:
- Observe that, in binary system, 1023=1111111111. That is, with 10 digits we can express up to number 1023.
This give us the idea to put in each envelope an amount of money equal to the positional value of each digit in the representation of 1023. That is, we will put the bills in envelopes with amounts of money equal to $1,$2,$4,$8,$16,$32,$64,$128,$256 and $512.
However, a little modification must be done, since we do not have $1023, only $1,000. To solve this, the last envelope should have $489 instead of 512.
Observe that:
- 1+2+4+8+16+32+64+128+256+489=1000
- Since each one of the first 9 envelopes represents a position in a binary system, we can represent every natural number from zero up to 511.
- If we want to give an amount "x" which is greater than $511, we can use our $489 envelope. Then we would just need to combine the other 9 to obtain x-489 dollars. Since
, by 2) we know that this would be possible.