Question

One number is four less than another number. If three times the smaller number is increased by the larger number, the result is twenty. Find the numbers.
A. x = 8; y = 12
B. x = 6; y = 2
C. x = 4; y = 8
D. x = 2; y = 6
The sum of three numbers is twenty. The first number is six more than two times the third number. The second number is eleven more than the product of the third number and three. Find the numbers.

A. x = 1.5; y = 6; z = 12.5
B. x = 0.5; y = 4.5; z = 15
C. x = 6.4; y = 8.1; z = 5.5
D. x = 7; y = 12.5; z = 0.5

3. The length of a rectangle is twenty-five kilometers less than four times the width. The perimeter is thirty-six kilometers. Find the length and the width.

A. l = 14.5; w = 3.5
B. l = 13.5; w = 4.5
C. l = 10.5; w = 7.5
D. l = 9.4; w = 8.6

4. One number is fifteen less than another number. If three times the larger number is decreased by the smaller number, the result is thirty. Find the numbers.

A. x = 15/2; y = 45/2
B. x = -15/2; y = 15/2
C. x = 22.5; y = 37.5
D. x = 7.5; y = 22

5. The perimeter of a rectangle is one hundred and fifty kilometers. The length of a rectangle is three more than five times the width. Find the length and the width.

A. l = 63; w = 12
B. l = 67.25; w = 15.5
C. l = 70; w = 5
D. l = 104; w = 29

Answer 1

x = y - 4
3x + y = 20
now sub y - 4 in for x in the 2nd equation
3(y - 4) + y = 20
3y - 12 + y = 20
4y = 20 + 12
4y = 32
y = 8
now sub 8 in for y in either equation to find x
x = y - 4
x = 8 - 4
x = 4
solution is : (4,8) -- answer C
======================
x + y + z = 20
x = 2z + 6
y = 3z + 11
now sub 2z + 6 in for x and 3z + 11 in for y
x + y + z = 20
(2z + 6) + (3z + 11) + z = 20
6z + 17 = 20
6z = 20 - 17
6z = 3
z = 3/6 which equals 0.5

x = 2z + 6
x = 2(0.5) + 6
x = 1 + 6
x = 7

y = 3z + 11
y = 3(0.5) + 11
y = 1.5 + 11
y = 12.5

solution is : (7,12.5,0.5) answer choice D
====================
P = 2L + 2W
P = 36
L = 4W - 25
now sub
36 = 2(4W - 25) + 2W
36 = 8W - 50 + 2W
36 + 50 = 10W
86 = 10W
86/10 = W
8.6 = W

L = 4W - 25
L = 4(8.6) - 25
L = 34.4 - 25
L = 9.4
answer choice D
=================
x = y - 15
3x - y = 30
now sub y - 15 in for x in the other equation
3(y - 15) - y = 30
3y - 45 - y = 30
2y = 75
y = 37.5
now sub 37.5 in for y in either equation to find x
x = y - 15
x = 37.5 - 15
x = 22.5
answer choice C
===================
P = 2L + 2W
P = 150
L = 5W + 3
now we sub
150 = 2(5W + 3) + 2W
150 = 10W + 6 + 2W
150 - 6 = 12W
144 = 12W
144/12 = W
12 = W
now sub 12 in for W
L = 5W + 3
L = 5(12) + 3
L = 60 + 3
L = 63
answer choice A