more math questions.. really sorry..?

Question

1) Jay's salary is 2/3 of his wife's salary. In Jan., wen they both get $2000 raises, their combined income will be $49000. What are their current incomes?

2) A width of a rectangle is 6 cm less than the length. A second rectangle, with a perimeter of 54 cm, is 3 cm wider and 2 cm shorter than the first. What are the dimensions of each rectangle?

3) Victor earns $3 an hr working after school and $4 an hour wokring on Saturdays. Last week he earned $43, working a total of 13 hrs. How many hours did he work on Saturday?

could u show me how you did the question? thanks so much.

Answer 1

It seems like you are asking alot of word problem questions. Try to assign variables to each item in the question that you need to figure out. Then make an equation with those variables and the numbers from the problem.

I'll help with the first one.

"Jay's salary is 2/3 of his wife's salary."
so...
Wife's salary = x (just choose a variable)
Jay's salary = 2/3 * x or just 2/3 x (2/3 of his wife's)

"In Jan., wen they both get $2000 raises, their combined income will be $49000."

Jay's (2/3x) + $2000 + wife's (x) + $2000 = $49000
2/3x + 2000 + x + 2000 = 49000
x + 2/3x + 4000 = 49000
5/3x = 45000
5x = 135000 (multiply both sides by 3)
x = 27000 (divide both sides by 5)

What are their current incomes?
*tricky question, they have NOT gotten their Jan. raises yet.*

Wife's salary = x = $27000
Jay's salary = 2/3x = $18000 (27000 x 2/3)

So just read your questions, and try to make an equation out of them.

Good luck!

Answer 2

1. Let Jay's salary be j and his wife's salary be b for better paid, therefore j = (2/3)b

After their $2,000 raises, their combined income will be $49,000, therefore, (j + 2000) + (b + 2000) = 49000

so, substitute from the first equation into the second:

j = (2/3)b
(j + 2000) + (b + 2000) = 49000
((2/3)b + 2000) + (b + 2000) = 49000
((2/3)b + 2000) + ((3/3)b + 2000) = 49000
(5/3)b + 4000 = 49000
(5/3)b = 45000
b = 27000
therefore, j = (2/3)b, so j = 18000

Jay currently makes $18,000, his wife makes $27,000


2. In the first rectangle, the width is W, the length is L and so W = L-6

In the second rectangle, the perimeter is 54 cm and its width and length are 3 cm wider and 2 cm shorter than the first. Therefore, W2 = W + 3 and L2 = L - 2 and 2 * (W2 + L2) = 54

So, the equations are:
W = L - 6
W2 = W + 3
L2 = L - 2
2 * (W2 + L2) = 54

So, substituting into the second equation:
W2 = (L - 6) + 3
W2 = L - 3
and substituting into the fourth equation:
2 * ((L - 3) + (L - 2)) = 54
2 * (2L - 5) = 54
4L - 10 = 54
4L = 64
L = 16 cm

So, since W = L - 6:
W = 16 - 6 = 10 cm
and since W2 = W + 3:
W2 = 10 + 3 = 13 cm
and since L2 = L - 2:
L2 = L - 2 = 16 - 2 = 14 cm

So, the dimensions of the first rectangle are width 10 cm, length 16 cm, and the dimensions of the second rectangle are width 13 cm and length 14 cm.


3) Victor's money = 43 for 13 hours at 3/hour and 4/hour

So, let A be the number of after school hours and S be the number of Saturday hours, so the equations are:

A + S = 13
3A + 4S = 43

Do the same here, substitute into the second equation the information from the first equation, like so:

A = 13 - S
So,
3 * (13 - S) + 4S = 43
39 - 3S + 4S = 43
S + 39 = 43
S = 43 - 39 = 4
So,
A = 13 - S = 13 - 4 = 9

So, Victor worked 4 hours on Saturday and 9 hours after school.

Answer 3

let J be the salary of Jay. and W be the salary of his wife
J = (2/3)W

the both get $2000 raise.
(J + 2000) + (W + 2000) = 49,000

J + W + 4000 = 49000
J + W = 4500

J = 2/3W

(2/3)W + W = 45000
(5/3)W = 45000
W = $27,000

J = (2/3) (27000)
J = $18,000



Let W be the width and L be the length
W = L - 6

let x be the width and y be the length of the second rectanlge
x = W + 3
y = L - 2

P = 2(W + L)
P = 2(x + y)
54 = 2(W + 3 + L - 2)

we know that W = L - 6
54 = 2 (L - 6 + 3 + L - 2)
27 = 2L - 5
32 = 2L
L = 16cm

W = 16 - 6
W = 10cm

x = W + 3
x = 10 + 3
x = 13cm

y = L - 2
y = 16 - 2
y = 14

The demention of the first rectangle is 16cm x 10cm
the dementions of the second rectangle is 13cm x 14cm




3) let t be the number of hours Victor worked after school. Then 13 - t is the number of hours he worked on Saturday

3t + 4(13 - t) = 43
3t + 52 - 4t = 43
-t = -9
t = 9

13 - 9 = 4

he worked 4 hrs on Saturday

Answer 4

(1) Total of the raises = $4000. Total income before raises = $49000 - 4000 = $45000. In terms of wifes' salary (1), total salary = 1+ 2/3 or 5/3. Divide $45000 by 5/3 to determine wife's salary. In other words, multiply it by 3 and divide by 5.
Answer = $27,000. Jay's salary would be 2/3 of that or $18,000. Total = $45,000 (check)

(2) Let width of first rectangle be w. Length will be w+6. Width of second rectangle would be w+3, and its length (w+6) -2 or w+4. Perimeter of 54 is equal to 2(w+3)+2(w+4).
Simplify: 2w+6+2w+8 = 4w+14 = 54. Subtract 14 from both sides, then divide both sides by 4. You will get w = 10. Now go back to the first rectangle and write down its dimensions, then do the second rectangle from that.

(3) Let the number of hours worked on Saturday = n, and the number worked on weekdays would be 13-n. Now multiply each of those by the wage rate: 4n + 3(13-n) = 43. Simplify, and you get 4n+39-3n = 43. Collect terms, subtract 39 from both sides: n = 4. He worked 4 hours on Saturday.

Answer 5

1)$49000-$4000=$45000
$45000/5=$9000
$9000*2=$18000
$18000+$2000=$20000
$49000-$20000=$29000
Jay has $20000 and wife has $29000
2)large rectangle has a width of 14cm and height of 13cm
width14cm +3=17 height13-2=11 17-11=6
so small rectangle width 17cm and height of 11 cm
3)x+y=13hrs 3x+4y=43 (4*4)+(9*3)=$43
so he worked 4 hours on saturday

Answer 6

1) x + 2000 + 2/3x + 2000 = 49000, or 5/3x = 45000, so x = 27000 (wife); 18000 (Jay)

3) 4x + 3*(13 - x) = 43, or x + 39 = 43, so x = 4

2) w = l - 6, and
2*(l - 6 + 3) + 2*(l -2 ) = 54, or 2l - 6 + 2l - 4 = 54, or 4l = 64, l =16
first: l = 16, w = 10
second: l = 14, w = 13