Everything Maths Grade 10

6.Solve the following simultaneous equations:

a) 7 x+ 3y= 13and 2 x 3 y= 4 b)10 = 2x+yandy=x 2

c) 7 x41 = 3yand17 = 3xy d) 2 x 4 y= 32and 7 x+ 2y= 32

e) 7 x+ 6y= 18 and 4 x+ 12y= 24 f) 3 x 4 y= 15 and 12 x+ 5y= 66

g) x 3 y= 22 and 5 x+ 2y= 25 h) 3 x+ 2y= 46and 15 x+ 5y= 220

i) 6 x+ 3y= 63 and 24 x+ 4y= 212 j) 5 x 6 y= 11and 25 x 3 y= 28

k)  9 x+ 3y= 4and 2 x+ 2y= 6 l) 3 x 7 y= 10 and 10 x+ 2y= 6

m) 2 y=x+ 8and 4 y= 2x 44 n) 2 a(a1)4 +ab= 0and 2 a^2 a=b+ 4

o)y= (x2)^2 andx(x+ 3)y= 3x+ 4(x1)p)

x+ 1

y

= 7and

x

y+ 1

= 6

q)(x+ 3)^2 + (y4)^2 = 0

7.Find the solutions to the following word problems:

a)^78 of a certain number is 5 more than^13 of the number. Find the number.

b)Three rulers and two pens have a total cost of R 21,00. One ruler and one pen have a total cost of

R 8,00. How much does a ruler cost and how much does a pen cost?

c)A group of friends is buying lunch. Here are some facts about their lunch:

• a hotdog costs R 6 more than a milkshake


• the group buys 3 hotdogs and 2 milkshakes


• the total cost for the lunch is R 143
  Determine the individual prices for the lunch items.
  d)Lefu and Monique are friends. Monique takes Lefu’s business studies test paper and will not tell
  him what his mark is. She knows that Lefu dislikes word problems so she decides to tease him.
  Monique says: “I have 12 marks more than you do and the sum of both our marks is equal to 166.
  What are our marks?”
  e)A man runs to the bus stop and back in 15 minutes. His speed on the way to the bus stop is 5 km·h^1
  and his speed on the way back is 4 km·h^1. Find the distance to the bus stop.
  f)Two trucks are travelling towards each other from factories that are 175 km apart. One truck is
  travelling at 82 km·h^1 and the other truck at 93 km·h^1. If both trucks started their journey at the
  same time, how long will they take to pass each other?
  g)Zanele and Piet skate towards each other on a straight path. They set off 20 km apart. Zanele skates
  at 15 km·h^1 and Piet at 10 km·h^1. How far will Piet have skated when they reach each other?
  h)When the price of chocolates is increased by R 10, we can buy five fewer chocolates for R 300.
  What was the price of each chocolate before the price was increased?
  i)A teacher bought R 11 300 worth of textbooks. The text books were for Science and Mathematics
  with each of them being sold at R 100 per book and R 125 per book respectively. If the teacher
  bought 97 books in total, how many Science books did she buy?
  j)Thom’s mom bought R 91,50 worth of easter eggs. The easter eggs came in 3 different colours blue,
  green and yellow. The blue ones cost R 2 each, green ones R 1,50 each and yellow ones R 1 each.
  She bought three times as many yellow eggs as the green ones and 72 eggs in total. How many
  blue eggs did she buy?
  k)Two equivalent fractions both have their numerator as one. The denominator of one fraction is the
  sum of two and a number, while the other fraction is twice the number less 3. What is the number?

8.Consider the following literal equations:

a)Solve forx:abx=c

Chapter 4. Equations and inequalities 103