Math question

1) During a closing down sale, a watch was sold at $143. the shopkeeper made a loss of 35% on the price he paid for it. Calculate his cost price for the watch.

Method 1:
Let $y be the cost price of the watch.
y(1 - 35%) = 143
y = 220
Cost price of the watch = $220

Method 2:
Cost price of the watch
= $143 ÷ (1 - 35%)
= $220


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2) Two similar solids have a base areas of 28 cm² and 63 cm². Find the mass of the larger solid if the mass of the smaller solid is 160g.

(Radius of the smaller solid) : (Radius of the larger solid)
= √28 : √63
= 2√7 : 3√7
= 2 : 3

(Mass of the smaller solid) : (Mass of the larger solid)
= (Volume of the smaller solid) : (Volume of the larger solid)
= 2³ : 3³
= 8 : 27

Mass of the larger solid
= 160 x (27/8) g
= 540 g


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3) Sector A , with an area of 150 cm² is cut out from a piece of paper. Find the area of sector B, with twice the radius r ,of sector A but half the size of angle x.

Area of sector A:
πr²(x/360) = 150

Area of sector B
= π(2r)²[(x/2)/360] cm²
= 2πr²(x/360) cm²
= 2(150) cm²
= 300 cm²