Answer to Question #122648 in Algebra for khomotso

Question

1.phiwe bought a packed of bananas she shred half of with her cousin then she shared her half of the bananas equally with her brother again. Now phiwe has 3 bananas. How many bananas were in the packet.
2. Phumza bought 12 metres of curtaining. Some of the material came from a roll with a slight flaw in it and cost R7 per metre instead of the normal R8 per metre. If phumza paid R98,50 altogether, how many metres of the damaged material did she buy?
3.Nancy buys 15 of ribbons . Her sister buys 6 metres of less ribbons but pays twice per metre. Between them the pay R6,00 .what is the price per metre of the two different types of ribbons?
4. You bought 10 shirts , some at R4,00 and some at R4,50 each. If the total cost was R43,50 , how many of each type did you buy?

Answer 1

1.

Solution.

Let x be amount of bananas in the packet,

x/2 be amount of bananas, phiwe had after she shared with her cousin,

(x/2)/2 = x/4 be amount of bananas, phiwe had after she shared with her brother.

we receive:

x/4 = 3

x = 3 * 4

x = 12

Answer: 12

2.

Solution.

Let x be amount of metres of the damage material,

y be amount of metres of the normal material.

From the conditions of the question we will receive the system of two equations:

x + y = 12 (1)

7x + 8y = 98.50 (2)

from equation (1) we receive:

y = 12 - x.

Now substitute y into equation (2):

7x + 8*(12 - x) = 98.5

7x + 96 - 8x = 98.50

-x = 98.5 - 96

-x = 2.5

x = -2.5

From conditions of the question we get Phuzma bought (-2.5) metres of the damage material. This statement is meaningless, that means there is a mistake in this question.

Answer: she bought -2.5 metres of the damaged material

3.

Solution.

"Between them the pay R6,00" means a difference between how much did Nancy pays and her sister.

Let x be the price per metre of ribbbons, Nancy buys, then

2x is the price per metre of ribbons, her sister buys.

From the condition of the question we will receive an equation:

15*x - 6*2x = 6

15x - 12x = 6

3x = 6

x = 6/3

x = 2

2x = 2 * 2 = 4

Then R2.00 is the price per metre of ribbons, Nancy buys,

R4.00 is the price per metre of ribbons, her sister buys.

Answer: R2.00 is the price per metre of ribbons, Nancy buys,

R4.00 is the price per metre of ribbons, her sister buys.

4.

Solution.

Let x be the amount of shirts at R4,00,

y be the amount of shirts at R4,50.

From the condition of the question we will receive a system of two equations:

x + y = 10 (1)

4*x + 4.5 *y = 43.5 (2)

from equation (1) we receive:

y = 10 - x

Now substitute y into equation (2):

4x + 4.5*(10 - x) = 43.5

4x + 45 - 4.5x = 43.5

-0.5x = 43.5 - 45

-0.5x = -1.5

x = -1.5/(-0.5)

x = 3,

then y =10 - x = 10 - 3 = 7

Answer: I bought 3 shirts at R4,00 and 7 shirts at R4,50.