Page 42 - Algebra

24 × 3 = y – 3
72 + 3 = y
y = 75
4. (x + 2) (y – 3) = xy – 20
xy – 3x + 2y – 6 = xy – 20 –3x + 2y = –14
3x – 2y = 14......................(1) (x – 1) (y + 2) = xy + 12
xy + 2x – y – 2 = xy + 12
2x – y = 14......................(2) Multiply (2) by 2
4x – 2y = 28......................(3) (3) – (1)
x = 14
3x – 2y = 14
3(14) – 2y = 14
2y = 28
y = 14
5. Let the number of males be x
Let the number of females be y
x + y = 42000.............. (1)
1.04x + 1.07y = 44340.............. (2) Multiply (1) by 1.04
1.04x + 1.04y = 43680.............. (3) (3) – (2)
0.03y = 660
y = 22000
x = 20000
The y – x = 22000 – 20000 = 2000
6. Let the age of the younger sister be x
The age of the elder sister be y 𝑥 =0.75
𝑦+2 1 𝑥 =75
𝑦+2 100 𝑥=3
𝑦+2 4
4x = 3y + 6 4x – 3y = 6
𝑥−3 = 1 𝑦4
4x - 12 = y
4x – y = 12
Subtract the two equations
Fraction = 22 75
Page 41 of 177
Algebra I & II