WAEC Mathematics Question 2015 ( Essay Question Nine 9)

QUESTION 9

(a) The first term of an Arithmetic Progression (AP) is 8, the ratio of the 7th term to the 9th term is 5 : 8, find the common difference of the AP.

(b) A trader bought 30 baskets of pawpaw and 100 baskets of mangoes for N2,450.00. She sold the pawpaw at a profit of 40% and the mangoes at a profit of 30%. If her profit on the entire transaction was N855.00, find the; 

(i) cost price of a basket of pawpaw ; 

(ii) selling price of the 100 baskets of mangoes.

Solution

(a) Given that the first term = a = 8, 

ratio of 7th to 9th term  = 5:8 and 

common difference , d = ?

Using Un = a + (n-1)d

Where;

n=Number of terms

a = First term

d = Common difference.

The 7th term 

 ..........................(i)

The 9th term 

 ..........................(ii)

The ratio of 7th to 9th term;

ie.   = 5:8

Cross multiplying, we have 

8(8 + 6d) = 5(8 + 8d)

64 + 48d = 40 + 40d

Collecting liketerms, we have,

48d - 40d = 40 - 64

8d = -24

d = -3

(b) Let the cost price for pawpaw = p and mango = m

 30 baskets of pawpaw = 30 x p = 30p

100 baskets of mangos = 100 x p = 100m

Sum of the fruits = ₦2,450

 30p + 100m = ₦2,450

dividing through by 10, we have;

3p + 10m = 245................(i)

Note:  She sold the pawpaw at a profit of 40%. ie. 

 

Hence, her profit for selling 30 baskets of pawpaw = 12p

Also she sold the mangoes at a profit of 30%. ie.

Hence, her profit for selling 100 basketsof mangoes = 30m

But her profit on the entire transaction(sum) = ₦855

 12p + 30m = 855

Dividing through by 3, we have,

4p + 10m = 245.....................(ii)

Solving equation (i) and (ii) simultaniously, we have,

3p + 10m = 245......................(i)

4p + 10m = 285 .....................(ii)

Sbtracting equation (i) from (ii)

(4p - 3p) + (10m - 10m) = 285 - 245

p + 0 = 40

p = 40

Hence, the cost price for a basket of pawpaw(p) = ₦40.00

(ii) Selling price for 100 baskets of mangoes.

First we solve for the cost price  for a basket of mango by substitutung p = 40 into equation (i)

3p + 10m = 245

3(40) + 10m = 245

120 + 10m = 245

10m = 245 -120

10m = 125

m = ₦12.50

Hence, coat price for 100 baskets of mangoes = 100 x 12.5

= ₦1,250

Note: She made a profit of 30% for selling 100 baskets of mangoes,

Where, SP = Selling price

CP = Cost price

Cross multiplying, we have;

10(SP - 1250) = 3 x 1250

10SP - 12500 = 3750

10SP = 3750 + 12500

10SP = 16250

SP = 1625 

SP = ₦1625

 The selling price for 100 baskets of mangoes  = ₦1625