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📝 Translate English sentences into algebraic equations (13 MCQs)

📖 From Digital SAT Algebra • 3. Mathematical Models in Algebra • 13 questions available

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What is Translate English sentences into algebraic equations?

Definition:
Translating English sentences into algebraic equations is the process of converting verbal statements into mathematical expressions using variables, operations, and equality signs. Key words: 'is' or 'equals' becomes $=$ , 'sum' becomes $+$ , 'difference' becomes $-$ , 'product' becomes $\times$ , and 'quotient' becomes $\div$ .

Working:
For 'The difference between a number and 8 is 4', write $x - 8 = 4$ . Solve: $x = 12$ . For 'Five times a number plus 3 is 28', write $5x + 3 = 28$ , solve: $5x = 25$ , $x = 5$ .

Example:
Translate 'A number divided by 6 equals 9' to $x/6 = 9$ . Multiply by 6: $x = 54$ .

Reason:
This is the cornerstone of solving word problems, as it bridges the gap between language and mathematics.

Easy

Medium

Hard

📝 All Translate English sentences into algebraic equations MCQs

Q1. Which algebraic equation correctly represents the sentence: "Seven less than three times a number is 20"?

3x-7=20

✅

7-3x=20

3(x-7)=20

3x+7=20

💡 Difficulty: easy | ✅ Correct: A

📖 Explanation: The phrase "three times a number" translates to $3x$ , while "seven less than" means subtract 7 from that quantity. Therefore, the correct translation is $3x-7=20$ . The other choices reverse the subtraction or incorrectly distribute the phrase.

Q2. A teacher says, "The sum of a number and 12 is twice the number." Which equation best models the statement?

x+12=x/2

x+12=2x

✅

12x=2+x

2(x+12)=x

💡 Difficulty: easy | ✅ Correct: B

📖 Explanation: The word "sum" indicates addition, so a number $x$ and 12 give $x+12$ . The phrase "is twice the number" means this sum equals $2x$ . Hence $x+12=2x$ accurately preserves the relationship.

Q3. A parking lot charges a fixed entry fee plus Rs. 50 per hour. A driver pays Rs. 350 after $h$ hours. Which equation represents the situation?

50h+350=0

350h+50=350

50+50h=350

✅

50+350h=350

💡 Difficulty: medium | ✅ Correct: C

📖 Explanation: The fixed entry fee is represented by 50, while the hourly cost is $50h$ . Since the total payment is Rs. 350, the correct model is $50+50h=350$ . This requires identifying which quantity is fixed and which depends on time.

Q4. A rectangle has a length that is 4 cm greater than its width. Its perimeter is 36 cm. If the width is $w$ , which equation correctly models the situation?

w+(w+4)=36

2w+4=36

2[w+(w+4)]=36

✅

2w+4w=36

💡 Difficulty: medium | ✅ Correct: C

📖 Explanation: If the width is $w$ , the length is $w+4$ . A rectangle's perimeter includes two lengths and two widths, so the total is $2[w+(w+4)]$ . Setting this equal to 36 produces the correct equation.

Q5. A student translates "Five times the difference between a number and 8 is 45" as $5x-8=45$ . What is the best assessment of the student's equation?

A.It is correct because multiplication always comes before subtraction.

B.It is incorrect because the correct equation is

5(x-8)=45

. ✅

C.It is incorrect because the correct equation is

x-5(8)=45

D.It is correct because

5x-8

means five times the difference.

💡 Difficulty: medium | ✅ Correct: B

📖 Explanation: The phrase "difference between a number and 8" creates the grouped quantity $x-8$ . The phrase "five times" applies to the entire difference, so parentheses are required. Thus $5(x-8)=45$ , not $5x-8=45$ .

Q6. A school club has 8 more members than another club. Together they have 54 members. If $x$ represents the smaller club's membership, which equation should be used?

x+(x+8)=54

✅

8x=54

x+(x-8)=54

2x+54=8

💡 Difficulty: medium | ✅ Correct: A

📖 Explanation: The smaller club has $x$ members, so the larger club has $x+8$ members. Because their combined membership is 54, adding the two expressions gives $x+(x+8)=54$ . This model correctly connects the verbal relationship to the total.

Q7. A phone plan costs Rs. 600 per month plus Rs. 8 for each additional gigabyte used. One month the bill is Rs. 792. If $g$ is the number of additional gigabytes, which equation represents the bill?

8(g+600)=792

600g+8=792

600+8g=792

✅

600-8g=792

💡 Difficulty: medium | ✅ Correct: C

📖 Explanation: The monthly charge of Rs. 600 is fixed, while Rs. 8 is added for every additional gigabyte. Therefore, the variable charge is $8g$ , and the total bill is $600+8g=792$ . The other choices confuse fixed and variable quantities.

Q8. A number is increased by 25% and then the result is 10 greater than the original number. Which equation correctly expresses this relationship using $x$ for the original number?

x+25=10x

1.25x=x+10

✅

25x=x+10

1.25+x=10

💡 Difficulty: hard | ✅ Correct: B

📖 Explanation: Increasing $x$ by 25% produces $x+0.25x=1.25x$ . The statement says this new value is 10 greater than the original, so it equals $x+10$ . Therefore, $1.25x=x+10$ correctly models both steps.

Q9. A graph shows a line crossing the $y$ -axis at 6 and passing through $(2,14)$ . Which verbal statement could reasonably be represented by its equation?

A.A number multiplied by 4 is 6

B.A starting amount of 6 increases by 4 for each unit ✅

C.A starting amount of 4 increases by 6 for each unit

D.Six less than four times a number is 14

💡 Difficulty: hard | ✅ Correct: B

📖 Explanation: The graph has $y$ -intercept 6, representing an initial amount of 6. From $(0,6)$ to $(2,14)$ , the change is 8 over 2 units, giving a rate of 4. Thus $y=6+4x$ , matching the second statement.

Q10. A student hears: "Eight more than twice a number equals five less than three times the number." Which equation should the student write before solving?

2x+8=3x-5

✅

8x+2=5x-3

2(x+8)=3(x-5)

2x-8=3x+5

💡 Difficulty: hard | ✅ Correct: A

📖 Explanation: "Twice a number" is $2x$ , and "eight more than" gives $2x+8$ . On the other side, "three times the number" is $3x$ , and "five less than" gives $3x-5$ . Therefore, $2x+8=3x-5$ .

Q11. A worker receives a base payment of Rs. 900 and a bonus of Rs. 75 for every completed task. After completing some tasks, the total payment is Rs. 2,100. Which equation and interpretation are both correct?

900+75t=2100

, where

t

is completed tasks ✅

75+900t=2100

, where

t

is completed tasks

900t+75=2100

, where

t

is the bonus

75(t+900)=2100

, where

t

is completed tasks

💡 Difficulty: medium | ✅ Correct: A

📖 Explanation: The base payment remains Rs. 900 regardless of the number of tasks. Each task adds Rs. 75, represented by $75t$ . Therefore, total earnings are $900+75t$ , and setting this equal to Rs. 2,100 correctly models the situation.

Q12. A student says the sentence "The difference between twice a number and 9 is equal to 15" must be written as $2(x-9)=15$ . What error has the student made?

A.They treated 2 as an addition instead of multiplication.

B.They incorrectly applied 2 to both terms inside the difference. ✅

C.They should have divided 15 by 9 first.

D.They reversed the entire equation.

💡 Difficulty: medium | ✅ Correct: B

📖 Explanation: The expression "twice a number" is $2x$ , and then 9 is subtracted from that result. Therefore, the correct equation is $2x-9=15$ . Writing $2(x-9)$ incorrectly makes 9 part of the quantity being doubled.

Q13. Two consecutive integers have a sum of 91. If $x$ represents the smaller integer, which equation correctly models the situation and why is it better than $2x+1=91$ ?

x+(x+1)=91

, because consecutive integers differ by exactly 1 ✅

x+(x+2)=91

, because two integers are involved

2x+1=91

, because the second integer is

x+1

x(x+1)=91

, because consecutive numbers are multiplied

💡 Difficulty: hard | ✅ Correct: A

📖 Explanation: If $x$ is the smaller consecutive integer, the next integer must be $x+1$ . Their sum is therefore $x+(x+1)$ . Although $2x+1=91$ happens to simplify to the same equation, the explicit form better represents the original relationship.

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