Answer and solution to Algebra Worksheets #1

Welcome back to Algebra Worksheets.

Here’s the answer to the previous algebra worksheets.

If x = -3 and y = 2, what is the value of the expression 2X² – 5xy?

2X² – 5xy

= 2(-3)² – 5(-3)(2)

= 18 – (-30)

= 18 + 30

= 48

If a = 4 and b = 7, calculate the value of 7a³ + 3ab – 3a².

7a³ + 3ab – 3a²

= 7(4)³ + 3(4)(7) – 3(4)²

= 7(64) + 3(28) – 3(16)

= 448 + 84 – 48

= 580

Given p = 4 and q = 9. Find the value of 4p²q³ – 6p³ + 10q² – 5.

4p²q³ – 6p³ + 10q² – 5

= 4(4)²(9)³ – 6(4)³ + 10(9)² – 5

= 4(16)(729) – 6(64) + 10(81) – 5

= 4(11664) – 384 + 810 – 5

= 46656 – 384 + 810 – 5

= 47077

In Kids Birthday Cake Restaurant, 3 cheese cakes and 2 swiss rolls cost $22.40. But 4 cheese cakes and 3 swiss rolls cost $31.20. Calculate the price of a cheese cake and a swiss roll.

Let cheese cake = x

Let swiss roll = y

3x + 2y = $22.40 ---- 1

4x + 3y = $31.20 ---- 2

Multiply the equation 1 with 3

(3x + 2y = $22.40) ×3 and you will get

9x + 6y = $67.20 ---- 3

Multiply equation 2 with 2

(4x + 3y = $31.20) × 2 and you’ll get

8x + 6y = $62.40 ---- 4

Equation 3 – equation 4:

9x + 6y = $67.20 ---- 3

8x + 6y = $62.40 ---- 4

---------------------------

X = $5.20

Substitute x = $5.20 into equation 1

3x + 2y = $22.40

3($5.20) + 2y = $22.40

$15.60 + 2y = $22.40

2y = $22.40 - $15.60

2y = $6.80

y = $6.80/2

y = $3.40

Answer: A cheese cake cost $5.20 and a swiss roll cost $3.40

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