Algebraic expressions · Ages 13–14

A new subject on both sides or below the line worksheet

Part of: Formulae & algebraic fractions

In the print window, choose “Save as PDF” to download it. The answers print on the last page.

Algebraic expressions · Ages 13–14

Numsprite
numsprite.com

Name:Date:Score:／48

Write each answer in the space. For word problems, show your working and write a sentence answer.

13.x g of sugar goes into 360 g of water, and sugar is c = xx + 360 of the mix. With x as the subject: x = c1 − c; for c = 14, add g of sugar.
Fill in each blank
Working:
Answer:
14.A price P is the cost C plus a profit rC (r = 0.7): P = C + rC. Which is the formula with C as its subject?
- A. C = P − rC
- B. C = Pr
- C. C = P1 + r
- D. C = P − r
Choose the right answer
Working:
Answer:
15.Alone, A paints a fence in 13 hours; A and B together take 12 hours. With 1T = 1a + 1b (T together, a and b each alone), how long would B take alone, in hours?
Working:
Answer:
16.24 oranges are shared equally by x children and 5 adults, y each: y = 24x + 5. With x as the subject: x = − yy; when each gets 3, there are children.
Fill in each blank
Working:
Answer:
17.Put the steps of making x the subject of y = x + 16x − 2 in order.
- A. x(y − 1) = 2y + 16
- B. xy − x = 2y + 16
- C. y(x − 2) = x + 16
- D. x = 2y + 16y − 1
Write the letters in the right order
Working:
Answer:
18.300 g of sugar water holds 40 g of sugar. With x g more sugar added, sugar makes up x + 40x + 300 of it. How many grams must be added for sugar to be 15 of it?
Working:
Answer:

Show the answers and working

A new subject on both sides or below the line worksheet: Answers and working

1. 2, 8
Multiply both sides by x + 8: xy + 8y = 2, xy = 2 − 8y, x = 2 − 8yy.
2. 25, 4
Take 4 from both sides: 25x = y − 4; multiply by x, then divide by y − 4: x = 25y − 4.
3. 7, 16
Take 16 from both sides: 7x = y − 16; multiply by x, then divide by y − 16: x = 7y − 16.
4. 14, 2, 5
y(x + 2) = 5x + 14, xy − 5x = 14 − 2y, x(y − 5) = 14 − 2y, x = 14 − 2yy − 5.
5. 6, 7, 4
y(x + 7) = 4x + 6, xy − 4x = 6 − 7y, x(y − 4) = 6 − 7y, x = 6 − 7yy − 4.

Marking: 2 for the working, 1 for the answer, 1 for the sentence.

13. 360, 120
c(x + 360) = x, cx + 360c = x, x − cx = 360c, x(1 − c) = 360c, x = 360c1 − c. With c = 14: x = 360 ÷ (4 − 1) = 120 g.
14. C. C = P1 + r
P = C + rC = C(1 + r); divide both sides by 1 + r: C = P1 + r.
15. 156 hours
1b = 1T − 1a = 112 − 113 = 1156, so b = 1561 = 156.
16. 24, 5, 3
Multiply by x + 5: xy + 5y = 24, so x = 24 − 5yy. With y = 3: x = (24 − 5 × 3) ÷ 3 = 3.
17. C → B → A → D
Clear the denominator, open the bracket, gather the x terms on one side, take x out as a factor, then divide by y − 1.
18. 25 g
x + 40x + 300 = 15: 5(x + 40) = x + 300, so (5 − 1)x = 300 − 5 × 40 and x = 25.

Numsprite · numsprite.com/en/worksheets/formulae-and-algebraic-fractions/subject-appearing-twice-or-in-a-denominator