math please help explain!!

[Notoriousjae]

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1. The largest of five consecutive even integers is 2 less than twice the smallest. Which of the following is the largest integer?
A.16
B.18
C.12
D.20
E.10

answer= B

2. A river flows at 3 miles per hour. A man can row at 5 miles per hour in still water. If he rows 1 mile upstream and then floats back to the starting place, how many minutes will be required for the roundtrip?
A.30
B.42
C.50
D.60
E.65

answer=C

3. A florist bought some plants for $150.00. She sold enough at 75 cents each to meet the cost and has 100 plants left. How many plants were originally purchased?
A.150
B.250
C.300
D.350
E.400

answer=C

4. when 2 is added to numerator of the fraction y/x, the fraction=1/4. when 2 is added to the denominator of y/x, the fraction equals 1/5. what is y/x?
A.10/40
B.10/48
C.12/44
D.1/3
E.1/2

answer=B

 

[dat_student]

1. The largest of five consecutive even integers is 2 less than twice the smallest. Which of the following is the largest integer?
A.16
B.18
C.12
D.20
E.10

answer= B
.....

too many problems, I do the 1st one for now:

2n, 2n + 2, 2n + 4, 2n + 6, 2n + 8

2n + 8 = 2 (2n) - 2
2n + 8 = 4n - 2
2n = 10
n = 5

largest = 2n + 8 = 2(5) + 8 = 18 (answer choice B)

 

[Notoriousjae]

thank you 🙂

 

[tinman831]

2. A river flows at 3 miles per hour. A man can row at 5 miles per hour in still water. If he rows 1 mile upstream and then floats back to the starting place, how many minutes will be required for the roundtrip?
A.30
B.42
C.50
D.60
E.65

answer=C

If he can go 5 miles per hour and the river takes him in the opposite direction for 3 miles in one hour, he can row a net 2 miles per hour forward. So if he goes upstream 1 mile, it'll take 30 minutes. Then floats back for one mile at 3 miles per hour (trip back takes 20 minutes). Total trip time is 50 minutes.

 

[tinman831]

4. when 2 is added to numerator of the fraction y/x, the fraction=1/4. when 2 is added to the denominator of y/x, the fraction equals 1/5. what is y/x?
A.10/40
B.10/48
C.12/44
D.1/3
E.1/2

answer=B

(y+2)/x = 1/4......... x = 4(y+2) = 4y+8

y/(x+2) = 1/5......... y = (x+2)/5

plug y into the x equation

x = 4y+8 = 4[(x+2)/5] + 8
x = (4x+8)/5 + 40/5 = (4x+8+40)/5 = (4x +48)/5
x = (4x+48)/5
5x = 4x + 48
x = 48

plug 48 back into the y equation
y = (48+2)/5 = 10

y/x = 10/48

*edit* I solved the problem algebraically but egots post below mine shows an easier way.

 

[egots]

3-(150)(4/3)+100

4-i think for a problem like this its easiest to just look at the answer choices 1st before solving if you can find it then set up an equation..ull save a lot of time this way b/c instead of going through setting up equations just look at th answer add 2 to the numerator see what equals 1/4th then add 2 to the denominator see what equals 1/5th

 

[dat_student]

3-(150)(4/3)+100

....

👍

0.75x = 150
(3/4) x = 150
(1/4)x = 50
x = 200 << this is (150)(4/3)

200 + 100 left = 300
or
(150)(4/3) + 100 left = 300

 

[Notoriousjae]

thanks guys. really appreciate it.