Reasoning with Equations & Inequalities — Drills
Reasoning with Equations & Inequalities has 9 drill skills. Each one generates fresh questions every time, with a hint and full worked steps, so you can keep practising a single skill until it settles.
What these drills cover
These questions use 2 ideas from the course. Follow any of them for a definition, where it is taught, and what it leads to.
Solveword
Unlimited questions of this kind are generated in the app. Two examples:
Problem 1
Ivy thinks of a number, multiplies it by 3, then adds 11. The result is 41. What was the number?
Worked answer
10
3n + 11 = 41
3n = 30
n = 10
Problem 2
Kai thinks of a number, multiplies it by 5, then adds 8. The result is 23. What was the number?
Worked answer
3
5n + 8 = 23
5n = 15
n = 3
Consecutive
Unlimited questions of this kind are generated in the app. Two examples:
Problem 1
The sum of 2 consecutive integers is 45. Find the smallest.
Worked answer
22
n + (n+1) = 45
2n + 1 = 45
n = 22
Problem 2
The sum of 2 consecutive integers is 63. Find the smallest.
Worked answer
31
n + (n+1) = 63
2n + 1 = 63
n = 31
Twoparts
Unlimited questions of this kind are generated in the app. Two examples:
Problem 1
A 100 cm rope is cut into two pieces, one 3 times as long as the other. How long is the shorter piece?
Worked answer
25
s + 3s = 100
4s = 100
s = 25, and the longer piece is 75 ✓
Problem 2
A 128 cm rope is cut into two pieces, one 3 times as long as the other. How long is the shorter piece?
Worked answer
32
s + 3s = 128
4s = 128
s = 32, and the longer piece is 96 ✓
Translate
Unlimited questions of this kind are generated in the app. Two examples:
Problem 1
Which expression means "x subtracted from 4"?
- x - 4
- 4 - x
- x + 4
- 4x
Worked answer
4 - x
You start from the number it is subtracted FROM.
Answer: 4 - x
Problem 2
Which expression means "7 more than n"?
- 7 - n
- 7n
- n + 7
- n - 7
Worked answer
n + 7
"More than" adds.
Answer: n + 7
Inequalities
Unlimited questions of this kind are generated in the app. Two examples:
Problem 1
Priya has $100. A ticket costs $20 and snacks are $4 each. At most how many snacks?
Worked answer
20
20 + 4s ≤ 100
4s ≤ 80
s ≤ 20
You cannot buy part of a snack, so 20.
Problem 2
Jonah has $50. A ticket costs $15 and snacks are $7 each. At most how many snacks?
Worked answer
5
15 + 7s ≤ 50
7s ≤ 35
s ≤ 5
You cannot buy part of a snack, so 5.
Geometry
Unlimited questions of this kind are generated in the app. Two examples:
Problem 1
A rectangle's length is 5 more than its width, and its perimeter is 46. Find the width.
Worked answer
9
2w + 2(w + 5) = 46
4w + 10 = 46
4w = 36, so w = 9 and the length is 14 ✓
Problem 2
A rectangle's length is 4 more than its width, and its perimeter is 56. Find the width.
Worked answer
12
2w + 2(w + 4) = 56
4w + 8 = 56
4w = 48, so w = 12 and the length is 16 ✓
Ages
Unlimited questions of this kind are generated in the app. Two examples:
Problem 1
Rosa is 6 years older than Nina. In 3 years, their ages will sum to 38. How old is Nina now?
Worked answer
13
In 3 years: Nina is b + 3, Rosa is b + 9
(b + 3) + (b + 9) = 38
2b + 12 = 38
b = 13 — Nina is 13, Rosa is 19 ✓
Problem 2
Devon is 5 years older than Maya. In 5 years, their ages will sum to 29. How old is Maya now?
Worked answer
7
In 5 years: Maya is b + 5, Devon is b + 10
(b + 5) + (b + 10) = 29
2b + 15 = 29
b = 7 — Maya is 7, Devon is 12 ✓
Coins
Unlimited questions of this kind are generated in the app. Two examples:
Problem 1
A jar holds 25 coins, only nickels and dimes, worth $1.70. How many dimes are there?
Worked answer
9
5n + 10(25 - n) = 170
5n + 250 - 10n = 170
-5n = -80, so n = 16 nickels
Dimes: 25 - 16 = 9 ✓
Problem 2
A jar holds 30 coins, only nickels and dimes, worth $2.25. How many dimes are there?
Worked answer
15
5n + 10(30 - n) = 225
5n + 300 - 10n = 225
-5n = -75, so n = 15 nickels
Dimes: 30 - 15 = 15 ✓
Rounding
Unlimited questions of this kind are generated in the app. Two examples:
Problem 1
A school has 277 students going on a trip. Each bus holds 40. How many buses are needed?
Worked answer
7
277 ÷ 40 = 6.92
6 buses hold only 240 students
Round UP: 7 buses, because the extra 37 still need a ride.
Problem 2
A school has 245 students going on a trip. Each bus holds 45. How many buses are needed?
Worked answer
6
245 ÷ 45 = 5.44
5 buses hold only 225 students
Round UP: 6 buses, because the extra 20 still need a ride.