Theory question 108
Commercial Arithmetic(a) Ms. Maureen spent ¼ of her monthly income at a shopping mall, ⅓ at an open market and 2/5 of the remaining amount at a Mechanic workshop. If she had ₦225,000.00 left, find: (i) her monthly income; (ii) the amount spent at the open market.
(b) The third term of an Arithmetic Progression (A.P.) is 4m − 2n. If the ninth term of the progression is 2m − 8n, find the common difference in terms of m and n.
Show the model answer
(a) Let income = x. Mall + market = x/4 + x/3 = 7x/12; remainder = 5x/12
Mechanic = 2/5 × 5x/12 = x/6; left = 5x/12 − x/6 = x/4
(i) x/4 = 225,000 → x = ₦900,000
(ii) Open market = ⅓ × 900,000 = ₦300,000
(b) a + 2d = 4m − 2n and a + 8d = 2m − 8n
Subtract: 6d = −2m − 6n
d = −(m + 3n)/3 = −m/3 − n
In (a) the ¼ and ⅓ are fractions of the whole income; only the 2/5 is of the remainder.