y = 48--4 = 12 Substitute the value of y in equation (2) x-3 (12) - 6 = 0 x = 36 + 6 = 42Therefore, Mary's present age is 42 years and her daughter's age is 12 years
`DO THIS
Solve example-10 by the substitution method
.Example-11. A publisher is planning to produce a newThe point which corresponds totextbook. The fixed costs (reviewing, editing, typesettinghow much money you have to earnand so on) are ` 320000. Besides that, he also spendsthrough sales in order to equal theanother ` 31.25 in producing the book. The wholesalemoney you spent in production isprice (the amount received by the publisher) is ` 43.75break even point.per book. How many books must the publisher sell tobreak even, i.e., so that the cost of production will equalrevenues? Solution : The publisher breaks even when costs equal revenues. If x represents the number ofbooks printed and sold and y be the breakeven point, then the cost and revenue equations for thepublisher are Cost equation is given by y = 320000 + 31.25x (1) Revenue equation is given by y = 43.75x (2)Using the second equation to substitute for y in the first equation, we have 43.75x = ` 320000 + 31.25 x12.5x = ` 320000x = 32000012.5 = 25,600 Thus, the publisher will break even when 25,600 books are printed and sold. EXERCISE - 4.2
Form a pair of linear equations for each of the following problems and find their solution.
1. The ratio of incomes of two persons is 9 : 7 and the ratio of their expenditures is 4 : 3. If each them manages to save `2000 per month, find their monthly income.