PROBLEMS IN SIMPLE EQUATIONS.

568. 9.

569. 14.

573. £8 158.

575. 1000 men.

570. 12.

572. At 104 miles from London, and in 107 hours.

577. 173, 1437%, and 12,5 gallons.

571. 12.

574. 8 hours.

576. 10

days, and 45 days.

591. 65.

580. 23 days.

582. 3 miles, 3 yards.
584. 6 hours, and 3 hours.
586. 240 acres; 28s. an acre.
588. Awith £70; Bwith £130.
590. The man in 213, the wo-
man in 50 days.

592. The weight is 50 lbs.; and the prime cost 28s. per lb.

593. The times are as (m + 1)n: (n+1)m:;

mn(m+1)(n+1) 'p{m(n+1)+n(m+1)}'

608. 25 miles from M.
610. The sherry £2 a dozen,

the claret £3 a dozen.

613. 693 men.

615. 4 yards, and 5 yards.

616. 19 in the first mixture, and 1 : 4 in the second.

RATIO, PROPORTION, AND VARIATION.

a2

618. a4b4a-b2 is the greater if a and b are integers. 619. a3 + b3 a+b2 is the greater ratio.

2

628. y2=4ax.

b2
627. y2=2(x2—a2).

631. 2 gallons from the 1st, and 14 from the second.

630. I 2 is the ratio.

mcx2
(m + 1)a2

and of the ruby is

632. The value of the diamond is £

645. n{(a2+x2) — (n−3)ax}. 646. _{n

a+bl

662. -2, 664. n=14.

119

5

663. 207, 297, 387.

a{(r+1)(n−p+1)+m(p−q)}+b{(r+1)p−m(p−q)}.

665.

670. n(3n−1)2+n(n−1)(7n—2)

671. 25 terms.

672. The sum is £135 4s.; the last payment £5 38. 673. AB=7, BC=9, CD=11, DE=13, and EF-15 miles.