Need some help with some questions:

1) The sum of the digits of a two - digit are reversed the number is increased by 36. Find the number by solving a pair of simultaneous equations.

2) 3 bags and 4 pens cost $61, whereas 4 bags and 3 pens cost $63.60. Find the cost of a bag and 10 pens.

3) Two runners start from the same point at the same time. They will 4km apart at the end of 2 hours if they are running in opposite directions. Let x be the speed of the faster runner and y be the speed of the slower runner.

i. Write down a pair of simultaneous equations using the fact that distance = speed×time.

ii. Find their speeds.

In δabc shown below, ∠bac is congruent to ∠bca: triangle abc, where angles a and c are congruent given: base ∠bac and ∠acb are congruent. prove: δabc is an isosceles triangle. when completed (fill in the blanks), the following paragraph proves that line segment ab is congruent to line segment bc making δabc an isosceles triangle. (4 points) construct a perpendicular bisector from point b to line segment ac . label the point of intersection between this perpendicular bisector and line segment ac as point d: m∠bda and m∠bdc is 90° by the definition of a perpendicular bisector. ∠bda is congruent to ∠bdc by the definition of congruent angles. line segment ad is congruent to line segment dc by by the definition of a perpendicular bisector. δbad is congruent to δbcd by the line segment ab is congruent to line segment bc because consequently, δabc is isosceles by definition of an isosceles triangle. 1. corresponding parts of congruent triangles are congruent (cpctc) 2. the definition of a perpendicular bisector 1. the definition of a perpendicular bisector 2. the definition of congruent angles 1. the definition of congruent angles 2. the definition of a perpendicular bisector 1. angle-side-angle (asa) postulate 2. corresponding parts of congruent triangles are congruent (cpctc)