Question

a silly riddle
here is a riddle: \i am thinking of two numbers that add up to 5. the difference between them is 9. what are the two numbers?\

1. name any pairs of numbers whose sum is 5.
2. name any pairs of numbers whose difference is 9.
3. the riddle can be represented with two equations. write the equations.
4. solve the riddle. explain or show your reasoning.

a quilting project
to make a quilt, a quilter is buying fabric in two - colors, light and dark. he needs at least 9.5 yards of fabric total.
the light color costs $9 a yard. the dark color costs $13 a yard. the quilter can spend up to $110 on fabric.
here are two graphs to represent the two constraints.

1. write and inequality to represent the length constraint. let x represent the yards of light fabric and y represent the yards of dark fabric.

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Explanation:

A Silly Riddle

Step1: Definir variables

Sea \(x\) y \(y\) los dos números. Entonces \(x + y=5\) y \(x - y = 9\) (suponiendo \(x\geq y\)).

Step2: Sumar ecuaciones

Sumando las dos ecuaciones \((x + y)+(x - y)=5 + 9\). Esto se simplifica a \(2x=14\), entonces \(x = 7\).

Step3: Encontrar \(y\)

Sustituyendo \(x = 7\) en \(x + y=5\), tenemos \(7+y=5\), así que \(y=5 - 7=- 2\).

Respuesta a las preguntas del acertijo:

1. Algunos pares de números cuya suma es 5 son \((1,4)\), \((2,3)\).
2. Algunos pares de números cuya diferencia es 9 son \((10,1)\), \((11,2)\).
3. Las ecuaciones son \(x + y=5\) y \(x - y = 9\).
4. Los números son \(x = 7\) y \(y=-2\) como se mostró en los pasos anteriores.

A Quilting Project

Step1: Escribir la desigualdad de longitud

El cuilter necesita al menos 9.5 yardas de tela en total. Si \(x\) es la cantidad de tela de color claro y \(y\) es la cantidad de tela de color oscuro, entonces la desigualdad es \(x + y\geq9.5\).

Answer:

A Silly Riddle

1. ejemplos: \((1,4)\), \((2,3)\)
2. ejemplos: \((10,1)\), \((11,2)\)
3. \(x + y=5\), \(x - y = 9\)
4. \(x = 7\), \(y=-2\)

A Quilting Project

1. \(x + y\geq9.5\)