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Mathematical problems of ladder electricity price
(1)① If a≤50, the price will remain at 0.53a without adjustment.

(2) If 50 < a ≤ 200, the electricity price of 50 < a≤200 kW·h is increased by 0.03 yuan per kWh, that is, the unit price of this part is:

0.53+0.03=0.56 yuan, because it is step by step, so the unit price less than or equal to 50 degrees is still 0.53.

Therefore, the electricity payable is 0.53× 50+(a-50 )× 0.56 = 0.56a-1.5.

(3) If a > 200, the electricity price of the part exceeding 200 kw·h will increase by 0.0 1 yuan, that is, the unit price of this part will be 0.53+0.0 1=0.54 yuan.

0.53×50+(200-50)×0.56+(a-200)×0.54 = 0.54 a+2.5

(2) The electricity consumption of Teacher Zhang 10 in the current month is130kwh, which is in line with (1)②, so it is 0.56a- 1.5.

Substitute a= 130, 0.56a-1.5 = 0.56x130-1.5 = 71.3 (yuan).

(3) If 50 degrees is used, it should be paid: 0.53×50=26.5 yuan.

If 200 degrees is used, the cost should be 0.53× 50+(200-150 )× 0.56 =110.5 (yuan).

10 this month, the electricity bill payable by Mr. Zhang's family was 98. 18 yuan, showing that it was 200 degrees less. According to the formula (1)②,

0.56a- 1.5=98. 18

Solution, a= 178