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中一級數學題
發問:
請清楚,詳盡地列出所有步驟 1.Peter is 12 years old and his grandfather is 63 years old now.(a)After how many years' time will Peter's age be 1/4 of his grandfather's age?(b)How many years ago was grandfather's age 18 times Peter's?2.A shop sold 129 records by Alan and Anita with a total sales of $12615.... 顯示更多 請清楚,詳盡地列出所有步驟 1.Peter is 12 years old and his grandfather is 63 years old now. (a)After how many years' time will Peter's age be 1/4 of his grandfather's age? (b)How many years ago was grandfather's age 18 times Peter's? 2.A shop sold 129 records by Alan and Anita with a total sales of $12615. Each record by Alan and each record by Anita are sold at $110 and $95 respectively. How many records (a)by Alan has the shop sold? (b)by Anita has the shop sold?
最佳解答:
其他解答:
1(a) set years to n 12+n/63+n=1/4 4(12+n)=63+n 48+4n=63+n 4n-n=63-48 3n=15 n=5 // 証︰(12+5/63+5=17/68=1/4) [勿抄] 1(b) set years to n 63-n/12-n=18 63-n=18(12-n) 63-n=216-18n 18n-n=216-63 17n=153 n=9 // 証: (63-9/12-9=54/3=18) [勿抄] 2 Set Alan sold to n, Anita sold to a n+a=129 --1 a=129-n --2 110n+95a=12615 --3 2-->3 110n+95(129-n)=12615 110n+12255-95n=12615 15n=12615-12255 15n=360 n=24 (a) Alan shop sold 24 n+a=129 24+a=129 a= 105 (b)=105 // 証︰(110*24+95*105=2640+9975=12615) [勿抄]
中一級數學題
發問:
請清楚,詳盡地列出所有步驟 1.Peter is 12 years old and his grandfather is 63 years old now.(a)After how many years' time will Peter's age be 1/4 of his grandfather's age?(b)How many years ago was grandfather's age 18 times Peter's?2.A shop sold 129 records by Alan and Anita with a total sales of $12615.... 顯示更多 請清楚,詳盡地列出所有步驟 1.Peter is 12 years old and his grandfather is 63 years old now. (a)After how many years' time will Peter's age be 1/4 of his grandfather's age? (b)How many years ago was grandfather's age 18 times Peter's? 2.A shop sold 129 records by Alan and Anita with a total sales of $12615. Each record by Alan and each record by Anita are sold at $110 and $95 respectively. How many records (a)by Alan has the shop sold? (b)by Anita has the shop sold?
最佳解答:
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Q1: Peter is 12 years old and his grandfather is 63 years old now. (a)After how many years' time will Peter's age be 1/4 of his grandfather's age? (b)How many years ago was grandfather's age 18 times Peter's? (a) Let x be the number of years (12+x)/(63+x)=1/4 48+4x=63+x 3x=15 x=5 ∴ After 5 years' time will Peter's age be 1/4 of his grandfather's age. (b) Let y be the number of years (63+y)/(12+y)=18 63+y=216+18y -17y=153 y=-9 ∴ 9 years ago was grandfather's age 18 times Peter's. Q2: A shop sold 129 records by Alan and Anita with a total sales of $12615. Each record by Alan and each record by Anita are sold at $110 and $95 respectively. How many records (a)by Alan has the shop sold? (b)by Anita has the shop sold? (a) Let x and 129-x be the number of records by Alan and Anita have the shop sold 110x+95(129-x)=12615 110x-95x=360 15x=360 x=24 ∴ 24 records by Alan has the shop sold (b) 129-x =129-24 =105 ∴ 105 records by Anita has the shop sold其他解答:
1(a) set years to n 12+n/63+n=1/4 4(12+n)=63+n 48+4n=63+n 4n-n=63-48 3n=15 n=5 // 証︰(12+5/63+5=17/68=1/4) [勿抄] 1(b) set years to n 63-n/12-n=18 63-n=18(12-n) 63-n=216-18n 18n-n=216-63 17n=153 n=9 // 証: (63-9/12-9=54/3=18) [勿抄] 2 Set Alan sold to n, Anita sold to a n+a=129 --1 a=129-n --2 110n+95a=12615 --3 2-->3 110n+95(129-n)=12615 110n+12255-95n=12615 15n=12615-12255 15n=360 n=24 (a) Alan shop sold 24 n+a=129 24+a=129 a= 105 (b)=105 // 証︰(110*24+95*105=2640+9975=12615) [勿抄]
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