Two less than four times a number.
Three more than five times a number.
Six more than two times a number.
Seven less than three times a number.
Three times the sum of five and a number.
3 × (5 + x)
Twice the quantity of five less than a number.
2 × (x – 5)
Five times the quantity of four less than six times a number.
5 × (6 x – 4)
Half of the sum of six and four times a number.
½ × (6 + 4 x)
Let x be the larger of two numbers whose sum is nine. Find an expression for two less than the smaller number.
Larger Number: x
Smaller Number: (9–x)
(9–x) – 2
Let x be the smaller of two numbers whose sum is eight. Find an expression for three more than the larger number.
Smaller Number: x
Larger Number: (8–x)
3 + (8–x)
Let x be the smaller of two numbers adding to twelve. Find an expression for twice the larger number.
Smaller Number: x
Larger Number: (12–x)
2 × (12–x)
Let x be the larger of two numbers adding to twenty. Find an expression for three more than half of the smaller number.
Larger Number: x
Smaller Number: (20–x)
3 + (½ × (20–x))
3 + (10 – x/2)
Let x be the largest of four consecutive integers. Find an expression for the sum of these integers.
Largest Integer: x
Second Largest Integer: (x–1)
Second Smallest Integer: (x–2)
Smallest Integer: (x–3)
x + (x–1) + (x–2) + (x–3)
Let x be the smallest of three consecutive even integers. Find an expression for the largest integer plus five times the smallest.
Smallest Integer: x
Middle Integer: (x+2)
Largest Integer: (x+4)
(x+4) + (5 x)
Let x be the smaller of two numbers whose difference is six. Find an expression for the three times the sum of four and the larger number.
Smaller Number: x
Larger Number: (x+6)
Why ‘+6’ and not ‘–6’?
If the difference is six,
the larger number must be six units more than
the smaller number.
3 × (4 + (x+6))
3 × (x + 10)
Let x be the middle integer of three consecutive odd integers. Find an expression for the sum of twice the quantity of three less than the largest integer, and five more than the product of seven and the smallest integer.
Smallest Integer: (x–2)
Middle Integer: x
Largest Integer: (x+2)
2 × ((x+2) – 3) + (5 + (7 × (x–2)))
2
×
(x
–
1)
+
(5
+
(7 x
–
14))
(2 x
–
2)
+
(7 x
–
9)
Two numbers add up to sixteen. The larger number is three times as big as the smaller number. What are the numbers?
|
Smaller Number: x Larger Number: (16–x) | OR |
Larger Number: x Smaller Number: (16–x) |
| (16–x) = 3 x | x = 3 (16–x) | |
| x = 4 | x = 12 |
Two numbers add up to thirteen. The larger number is one more than twice the smaller number. What are the numbers?
|
Smaller Number: x Larger Number: (13–x) | OR |
Larger Number: x Smaller Number: (13–x) |
| (13–x) = 1 + 2 x | x = 1 + 2 (13–x) | |
| x = 4 | x = 9 |
Two numbers have a sum of twenty and a difference of six. What are the numbers?
|
One Number: x Other Number: (20–x) | ||
| x – (20–x) = 6 | OR | (20–x) – x = 6 |
| x = 13 | x = 7 |
Three consecutive integers have a sum of thirty-six. What are the integers?
|
Smallest Number: x Middle Number: x+1 Largest Number: x+2 | OR |
Largest Number: x Middle Number: x–1 Smallest Number: x–2 |
| x + (x+1) + (x+2) = 36 | x + (x–1) + (x–2) = 36 | |
| x = 11 | x = 13 |
Two numbers add up to twenty. The larger number is four less than three times the smaller number. What are the numbers?
|
Smaller Number: x Larger Number: (20–x) | OR |
Larger Number: x Smaller Number: (20–x) |
| (20–x) = 3 x – 4 | x = 3 (20–x) – 4 | |
| x = 6 | x = 14 |
Two numbers have a difference of ten. The smaller number is one less than a quarter of the larger number. What are the numbers?
|
Smaller Number: x Larger Number: (x+10) | OR |
Larger Number: x Smaller Number: (x–10) |
| x = (¼) (x+10) – 1 | (x–10) = (¼) x – 1 | |
| x = 2 | x = 12 |
Two numbers have a difference of five. The smaller number is three more than half of the larger number. What are the numbers?
|
Smaller Number: x Larger Number: (x+5) | OR |
Larger Number: x Smaller Number: (x–5) |
| x = 3 + (½) (x+5) | (x–5) = 3 + (½) x | |
| x = 11 | x = 16 |
One number is three times larger than another number. The larger number is also one less than twice the sum of three and the smaller number. What are the numbers?
|
Smaller Number: x Larger Number: 3 x |
| 3x = 2 (3 + x) – 1 |
| x = 5 |
A post office has 27 stamps in a folder. The folder contains 34¢ stamps and 20¢ stamps. The total value of the stamps in the folder is $8.20. How many of each type of stamp are in the folder?
| Quantity | Value | |
|
34¢ stamps: 20¢ stamps: |
x (27–x) |
34x cents 20(27–x) or (540–20x) cents |
| 34x + (540–20x) = 820 ←$8.20 converted to cents | ||
| x = 20 | ||
A collector has 14 guitars worth a total of $810. The accoustic guitars are worth $40 each, and the electric guitars are worth $90 each. How many of each type of guitar does the collector have?
| Quantity | Value | |
|
Accoustic: Electric: |
g (14–g) |
$40g $90(14–g) or $(1260–90g) |
| 40g + (1260–90g) = 810 | ||
| g = 9 | ||
A school spent $168 to buy 22 tickets for a museum field trip. Adult tickets cost $15 each, while student tickets each cost only $6. How many of each type of ticket were purchased?
| Quantity | Value | |
|
Adult Tickets: Student Tickets: |
t (22–t) |
$15t $6(22–t) or $(132–6t) |
| 15t + (132–6t) = 168 | ||
| t = 4 | ||
A jar contains 30 coins worth $3.90. The jar only holds quarters (25¢) and nickels (5¢). How many of each type of coin are in the jar?
| Quantity | Value | |
|
Quarters: Nickels: |
q (30–q) |
25q cents 5(30–q) or (150–5q) cents |
| 25q + (150–5q) = 390 ←$3.90 converted to cents | ||
| q = 12 | ||
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