Example Question - word problem
Here are examples of questions we've helped users solve.
Basic Arithmetic Problem on Summer Reading
<p>Let the total number of books Ada wants to read be \( T \).</p> <p>Let the number of books about cats be \( C \).</p> <p>Let the number of books about horses be \( H \).</p> <p>According to the problem, \( T = 12 \) and \( C = 5 \).</p> <p>To find \( H \), we subtract the number of books about cats from the total number of books:</p> <p>\( H = T - C \)</p> <p>\( H = 12 - 5 \)</p> <p>\( H = 7 \)</p> <p>Therefore, \( 7 \) books are stories about horses.</p>
Calculating the Number of Mollies in a Pet Fish Collection
<p>\text{Total pet fish} = 17</p> <p>\text{Goldfish} = 7</p> <p>\text{Let m be the number of mollies.}</p> <p>\text{Total pet fish} = \text{Goldfish} + \text{mollies}</p> <p>17 = 7 + m</p> <p>m = 17 - 7</p> <p>m = 10</p> <p>\text{Levi has 10 mollies.}</p>
Take-Apart Subtraction Word Problem
<p>Total potatoes = 9</p> <p>White potatoes = 4</p> <p>Red potatoes = Total potatoes - White potatoes</p> <p>Red potatoes = 9 - 4</p> <p>Red potatoes = 5</p>
Calculating the Distance Between Towns
<p>Let the distance from Jackson to Salem be \( J \).</p> <p>The distance from Salem to Bellevue is twice \( J \), so it is \( 2J \).</p> <p>The distance from Bellevue to Denton is \( 61 \) miles.</p> <p>Thus, the distance from Jackson to Denton is \( J + 2J + 61 \).</p> <p>Combine like terms: \( 3J + 61 \).</p> <p>The distance from Jackson to Denton is \( 3 \times 15 + 61 = 45 + 61 = 106 \) miles.</p>
Solving a Distance Problem
<p>선자는 물 위에 뜬 판 위에 1000리터 물까지 싣고 갈 수 있다고 그 물고기의 '솔직히' 말하자면 1200리터의 무게까지 실을 수 있다고 합니다.</p> <p>해결 방법은 다음과 같습니다:</p> <p>1. 선자가 실을 수 있는 최대 무게를 찾기 위해서 '솔직히' 말한 무게에서 실제로 실을 수 있는 무게를 빼줍니다.</p> <p>\[ 1200리터 - 1000리터 = 200리터 \]</p> <p>2. 선자는 200리터 더 실을 수 있다고 합니다.</p>
Fraction Comparison in a Word Problem
<p>문제의 내용을 바탕으로 달팽이와 거북이가 각각 얼마나 이동했는지 계산하여 비교하면 다음과 같습니다:</p> <p>달팽이는 \(\dfrac{1}{2}\) 만큼 이동, 거북이는 \(\dfrac{1}{3}\) 만큼 이동, 그리고 달팽이는 추가로 1200cm를 더 이동했습니다.</p> <p>달팽이와 거북이가 지나간 전체 거리를 \(x\)라고 하면:</p> <p>달팽이의 거리: \(\dfrac{1}{2}x + 1200\)</p> <p>거북이의 거리: \(\dfrac{1}{3}x\)</p> <p>거북이의 거리를 달팽이의 거리와 같게 만들어주기 위해 등식을 세웁니다:</p> <p>\(\dfrac{1}{3}x = \dfrac{1}{2}x + 1200\)</p> <p>분모를 통분하기 위해 양변에 6을 곱합니다:</p> <p>2x = 3x + 7200</p> <p>x를 한쪽으로 모읍니다:</p> <p>x = 7200</p> <p>따라서 달팽이와 거북이가 이동한 전체 거리는 7200cm입니다.</p> <p>달팽이가 이동한 거리를 구하면:</p> <p>\(\dfrac{1}{2} \times 7200 + 1200 = 3600 + 1200 = 4800cm\)</p> <p>거북이가 이동한 거리:</p> <p>\(\dfrac{1}{3} \times 7200 = 2400cm\)</p> <p>달팽이가 더 많이 이동한 거리를 구하려면 달팽이와 거북이의 거리 차이를 계산합니다:</p> <p>4800cm - 2400cm = 2400cm</p> <p>따라서 달팽이는 거북이보다 2400cm 더 많이 이동하였습니다.</p>
Algebraic Expression from a Word Problem
<p>Sea \(x\) el número desconocido.</p> <p>El triple del número se expresa como \(3x\).</p> <p>El triple de un número aumentado en cinco unidades se expresa como \(3x + 5\).</p>
Mountain Trip Distance Problem
<p>En total, Luis debe recorrer 3150 metros.</p> <p>En la primera etapa recorre 975 metros y en la segunda 1100 metros.</p> <p>Para calcular la distancia recorrida en la tercera etapa, sumamos las distancias de las dos primeras etapas y la restamos del total:</p> <p>Distancia en la tercera etapa = Total de distancia - (Distancia primera etapa + Distancia segunda etapa)</p> <p>Distancia en la tercera etapa = 3150 metros - (975 metros + 1100 metros)</p> <p>Distancia en la tercera etapa = 3150 metros - 2075 metros</p> <p>Distancia en la tercera etapa = 1075 metros</p> <p>Luis recorrerá 1075 metros en la tercera etapa.</p>
Finding the Ratio of Ages - Mother and Daughter
Para resolver la pregunta, debemos primero encontrar las edades actuales de Ana y su madre. Según el problema, hace 10 años, las edades de Ana y de su madre eran de 15 y 40 años, respectivamente. Entonces sumamos 10 años a ambas edades para obtener sus edades actuales: Edad actual de Ana = 15 años + 10 años = 25 años Edad actual de la madre de Ana = 40 años + 10 años = 50 años Ahora calculamos la razón entre las edades actuales de ambas: Razón = Edad de Ana / Edad de la madre Razón = 25 años / 50 años Razón = 1/2 Por lo tanto, la razón entre las edades actuales de Ana y su madre es de 1/2. La respuesta correcta es la opción c) 1/2.
Calculation of Candle Consumption Time
Para resolver esta pregunta, podemos establecer una relación de proporcionalidad directa entre la cantidad de vela consumida y el tiempo. Según el problema, sabemos que: - La vela mide originalmente 30 cm. - Después de estar encendida durante 12 minutos, la vela se reduce en 2,5 cm. Para hallar el tiempo total que se llevará en consumir toda la vela, usamos la siguiente proporción: 2,5 cm -- 12 minutos 30 cm -- x minutos Para resolver por x, podemos establecer la siguiente ecuación basándonos en la propiedad fundamental de las proporciones, es decir, que el producto de los medios es igual al producto de los extremos: 2,5 cm * x minutos = 30 cm * 12 minutos x = (30 cm * 12 minutos) / 2,5 cm x = 360 minutos / 2,5 x = 144 minutos Así que, para que se consuma toda la vela de 30 cm, se necesitarán 144 minutos. Por lo tanto, la respuesta correcta es la opción b) 144 minutos.
Age Word Problem Solution
The image contains a word problem that states: "Richard and Tom have a combined age of 49. Richard is 3 years older than twice Tom's age. How old are Richard and Tom?" We can turn this word problem into a system of equations with two variables, R for Richard's age and T for Tom's age. The first equation comes from the first sentence: R + T = 49 (Equation 1) The second sentence provides us with a second equation: R = 2T + 3 (Equation 2) With these two equations, we can solve for R and T. We can use the substitution method by substituting Equation 2 into Equation 1: (2T + 3) + T = 49 Just simplify and solve for T: 2T + T = 49 - 3 3T = 46 T = 46 / 3 T = 15.333... Since we are typically dealing with whole years for ages, rounding down to the nearest whole number wouldn't be conventionally correct for determining age, but it seems the question might have assumed whole numbers, so let's consider T as 15 for the purposes of this problem (though in real-world terms, the exact age could also be a fractional part of a year). Now we will solve for R using T = 15: R = 2(15) + 3 R = 30 + 3 R = 33 Therefore, Tom is 15 years old, and Richard is 33 years old.
Determining Distance to Dog Park
The image provides a word problem about James and Amber who walk their dogs together at a nearby dog park. They wish to determine who has to walk a farther distance to get to the dog park. The question requires the use of a coordinate plane to determine the distances, with the town square (origin) at (0,0), James's house at (1, -4), Amber's house at (2, -6), and the dog park at (2, 4). To find out how far each person lives from the dog park, you need to calculate the distance between their houses and the dog park using the distance formula for coordinates: Distance = √((x2 - x1)² + (y2 - y1)²) For James: Distance between James's house and the dog park = √((2 - 1)² + (4 - (-4))²) = √((1)² + (8)²) = √(1 + 64) = √(65) For Amber: Distance between Amber's house and the dog park = √((2 - 2)² + (4 - (-6))²) = √((0)² + (10)²) = √(0 + 100) = √(100) = 10 Comparing the two distances, √(65) is less than 10, which means James lives closer to the dog park than Amber. The statement to complete would therefore be: James is √(65) blocks from the dog park and Amber is 10 blocks from the dog park. This means that Amber is farther from the dog park.
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