問題

广州公交卡新政策,一个月内消费满80元后8折优惠,满200之后5折优惠,小明一个月工作26天,单程车费5元,请问小明一个月车费要多少钱?

思考

Interpreting monthly expenses

I’m working through Xiao Ming's monthly bus fare by calculating daily and monthly costs, ensuring the new discount policies are applied correctly to reach an accurate total.

Clarifying discount mechanics

I’m ensuring Xiao Ming's bus card policy is interpreted correctly: after an initial 80 RMB spend, subsequent rides are discounted to 80% until reaching 200 RMB, then further reduced to 50%.

Clarifying the discount strategy

First, Xiao Ming pays full fare until spending 80 RMB. Rides costing 0.8 times fare until 200 RMB, then 0.5 times fare beyond 200 RMB.

Calculating expenses

With 52 rides at 5 RMB each, the pre-discount cost is 260 RMB. The new policy applies discounts after reaching certain consumption thresholds.

Determining ride costs

I’m mapping out the number of rides at full, 80%, and 50% discounts. Calculating the total cost involves multiplying the number of discounted rides by their respective fares.

Estimating ride costs

I’m figuring out how many rides Xiao Ming can take at full price before reaching discounts. After 16 rides, he spends 80 RMB, making subsequent rides cheaper.

Calculating total expenses

I’m figuring out Xiao Ming's final ride costs: 6 rides at half price, adding 15 RMB, to the previous 215 RMB. The total cost is 215 RMB.

Confirming the total cost

OK, let me see: 16 rides at full price, 30 rides at a discount, and 6 rides at half price. The total cost is 215 RMB.

Reassessing ride costs

I’m piecing together the exact rides at full, discounted, and half-price. The total cost checks out at 215 RMB.

Reasoned about 小明的月度公交费,持续 22 秒

回答

小明一个月需要乘坐52次(26个工作日,每天往返2次)。

根据新政策,票价计算分为三个阶段:

  1. 前80元全价
    单程票价5元,要累计80元,全价乘车次数为

    805=16\frac{80}{5}=16 \text{次}

    此阶段费用:16 × 5 = 80元

  2. 80元至200元期间(8折,即每次4元)
    这一阶段需要消费:200 - 80 = 120元
    票价为4元/次,所以乘车次数为

    1204=30\frac{120}{4}=30 \text{次}

    此阶段费用:30 × 4 = 120元

  3. 累计消费超过200元后(5折,即每次2.5元)
    小明总乘车次数为52次,已乘车次数16 + 30 = 46次,剩余次数为

    5246=652 - 46 = 6 \text{次}

    此阶段费用:6 × 2.5 = 15元

总车费 = 80元 + 120元 + 15元 = 215元

因此,小明一个月的公交车费为215元。

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