💡First, identify the number of cucumbers, which is given as 58.Next, calculate the number of carrots by subtracting 24 from the number of cucumbers:58 - 24 = 34 carrots.Then, determine the number of tomatoes by adding 49 to the number of cucumbers:58 + 49 = 107 tomatoes.Since the number of radishes equals the number of carrots, there are also 34 radishes.Finally, sum all the quantities to find the total number of vegetables:58 (cucumbers) + 34 (carrots) + 107 (tomatoes) + 34 (radishes) = 233.

💡First, I need to determine the average of the first 6 numbers out of 10, given that the overall average is 60 and the average of the last 6 numbers is 75. The 7th number is provided as 258.I'll start by calculating the total sum of all 10 numbers using the overall average:Total sum = 10 × 60 = 600Next, I'll find the sum of the last 6 numbers based on their average:Sum of last 6 numbers = 6 × 75 = 450Since the 7th number is included in both the first 6 and the last 6 numbers, I need to adjust for this overlap. I'll subtract the 7th number from the sum of the last 6 numbers to find the sum of the first 6 numbers:Sum of first 6 numbers = Sum of last 6 numbers - 7th numberSum of first 6 numbers = 450 - 258 = 192Finally, I'll calculate the average of the first 6 numbers by dividing the sum by 6:Average of first 6 numbers = 192 ÷ 6 = 32Therefore, the average of the first 6 numbers is 32.

💡First, I need to determine the initial number of members in family e, denoted as E.The total number of family members before any left for the hostel is the sum of members in all families: 7 (a) + 8 (b) + 10 (c) + 13 (d) + E (e) + 10 (f).After one member from each family leaves, the number of members in each family becomes: 6 (a) + 7 (b) + 9 (c) + 12 (d) + (E - 1) (e) + 9 (f).The average number of members in each family after one member leaves is 8, and with 6 families, the total number of members becomes 6 families * 8 members/family = 48 members.Setting up the equation with the total number of members after one member leaves:6 + 7 + 9 + 12 + (E - 1) + 9 = 48.Combining the known numbers:43 + (E - 1) = 48.Solving for E:E - 1 = 5E = 6.Therefore, there were initially 6 members in family e.

💡First, I need to define the variables for the length and width of the hall. Let’s denote the length as ( L ) and the width as ( W ).According to the problem, the width is half of the length, which can be expressed as:[ W = frac{1}{2}L ]It is also given that the difference between the length and the width is 12 units:[ L - W = 12 ]To find the value of ( L ), I can substitute the expression for ( W ) from the first equation into the second equation:[ L - frac{1}{2}L = 12 ]Simplifying this equation:[ frac{1}{2}L = 12 ]Multiplying both sides by 2 to solve for ( L ):[ L = 24 ]Now that I have the length, I can find the width using the first equation:[ W = frac{1}{2} times 24 = 12 ]Finally, to find the area of the hall, I multiply the length by the width:[ text{Area} = L times W = 24 times 12 = 288 ]Therefore, the area of the hall is 288 square units.

💡To determine the largest number of mogs Bill can purchase while spending exactly 100 and buying at least one of each item, we start by setting up the equation for the total cost:[3x + 4y + 8z = 100]where ( x ), ( y ), and ( z ) represent the number of mags, migs, and mogs respectively, and all are at least 1.First, we substitute the minimum values for ( x ) and ( y ) to maximize ( z ):[3(1) + 4(1) + 8z = 100 3 + 4 + 8z = 100 8z = 93 z = frac{93}{8} approx 11.625]Since ( z ) must be an integer, we try ( z = 11 ):[8(11) = 88 3x + 4y = 100 - 88 = 12]We need to find integer values for ( x ) and ( y ) such that ( 3x + 4y = 12 ) with ( x, y geq 1 ). Testing possible values:- ( x = 2 ), ( y = 1 ): ( 3(2) + 4(1) = 10 ) (Not enough)- ( x = 1 ), ( y = 2 ): ( 3(1) + 4(2) = 11 ) (Still not enough)- ( x = 1 ), ( y = 1 ): ( 3(1) + 4(1) = 7 ) (Does not satisfy)Since ( z = 11 ) is not feasible, we try ( z = 10 ):[8(10) = 80 3x + 4y = 100 - 80 = 20]Testing possible values for ( x ) and ( y ):- ( x = 2 ), ( y = 3 ): ( 3(2) + 4(3) = 18 ) (Close, but not enough)- ( x = 1 ), ( y = 4 ): ( 3(1) + 4(4) = 19 ) (Still not enough)- ( x = 1 ), ( y = 5 ): ( 3(1) + 4(5) = 23 ) (Exceeds 20)The correct values are ( x = 4 ) and ( y = 2 ):[3(4) + 4(2) = 12 + 8 = 20]Thus, Bill can buy 4 mags, 2 migs, and 10 mogs.

💡Alright, so I've got this problem here about Uncle Li and Aunt Lin contracting rice fields. Let me try to understand what's being asked and figure out how to solve it step by step.First, the problem says Uncle Li contracted 12 acres of rice fields, and each acre yields 660 kilograms of rice. Aunt Lin contracted 2 acres less than Uncle Li, so that would be 10 acres. It also mentions that the total rice yield of Aunt Lin is 420 kilograms less than that of Uncle Li. Okay, so the first question is asking for the total yield of Uncle Li's rice in kilograms. That seems straightforward since we know the number of acres he contracted and the yield per acre. I think I can calculate that by multiplying the number of acres by the yield per acre.So, for Uncle Li:Total yield = Number of acres × Yield per acreTotal yield = 12 acres × 660 kg/acreLet me do that multiplication. 12 times 660... Hmm, 10 times 660 is 6600, and 2 times 660 is 1320. Adding those together, 6600 + 1320 equals 7920. So, Uncle Li's total yield is 7920 kilograms.Now, the second question is a bit trickier. It asks how much less the yield per acre of Uncle Li's rice is compared to Aunt Lin's. So, I need to find the yield per acre for both Uncle Li and Aunt Lin and then find the difference between them.We already know Uncle Li's yield per acre is 660 kg. For Aunt Lin, she has 10 acres, and her total yield is 420 kg less than Uncle Li's. Since Uncle Li's total yield is 7920 kg, Aunt Lin's total yield would be 7920 - 420 = 7500 kg.Now, to find Aunt Lin's yield per acre, I'll divide her total yield by the number of acres she contracted:Yield per acre = Total yield / Number of acresYield per acre = 7500 kg / 10 acresCalculating that, 7500 divided by 10 is 750. So, Aunt Lin's yield per acre is 750 kg.Now, to find out how much less Uncle Li's yield per acre is compared to Aunt Lin's, I'll subtract Uncle Li's yield per acre from Aunt Lin's:Difference = Aunt Lin's yield per acre - Uncle Li's yield per acreDifference = 750 kg/acre - 660 kg/acreThat gives me a difference of 90 kg per acre. So, Uncle Li's yield per acre is 90 kg less than Aunt Lin's.Wait, let me double-check my calculations to make sure I didn't make any mistakes. For Uncle Li's total yield, 12 times 660 is indeed 7920. Aunt Lin's total yield is 7920 minus 420, which is 7500. Dividing 7500 by 10 gives 750 kg per acre. Subtracting 660 from 750 gives 90. Yeah, that seems correct.I think I've got it. Uncle Li's total yield is 7920 kg, and his yield per acre is 90 kg less than Aunt Lin's.