A person invested $8300 for 1 year, part at 7%, and the remainder at 12%. The total annual income from these investment was $898. The amount of money invested at 12% was $700 more than the amounts invested at 7% and 11% combined. Find the amount invested at each rate.
$1500 at 7%
$2300 at 11%
$4500 at 12%
It takes \( 8 \) minutes for Byron to fill the kiddie pool in the backyard using only a handheld hose. When his younger sister is impatient, Byron also uses the lawn sprinkler to add water to the pool so it is filled more quickly. If the hose and sprinkler are used together, it takes \( 5 \) minutes to fill the pool. Which equation can be used to determine r; the rate in parts per minute, at which the lawn sprinkler would fill the pool if used alone?
\( \frac { 5 } { 8 } + 5 r = 8 \)
\( \frac { 5 } { 8 } + 5 r = 1 \)
\(5 ( \frac { 5 } { 8 } ) = r \)
\( \frac { 5 } { 8 } = 5 r\)
Mike and Jamal are \( 9 \) miles apart, and are planning to meet up. Mike is walking at an average speed of \( 3 \) miles per hour to meet Jamal. Jamal is driving at an average speed of \( 25 \) miles per hour to meet Mike.
Which equation can be used to find \( t \) , the time it takes for Mike and Jamal to meet?
\(25 t - 3 t = 0 \)
\( 25 t - 3 t = 9 \)
\( 25 t + 3 t = 1 \)
\( 25 t + 3 t = 9\)
On a map, each inch represents \( 6.5 \) miles. What is the distance represented by \( 6 \) inches?
Step \( 1 \) of 2: Set up the proportion for the word problem. Use \( x \) as the unknown variable.
Ali's latest photo got \( 42 \) likes. This is \( 3 \) times as many likes as Kate's latest photo. How many likes did Kate's photo get? Select the correct solution method below, using \( x \) to represent Kate's likes.
A. \( 3 x = 42 \) . Divide both sides by \( 3 \) . Kate's photo got \( 14 \) likes.
B. \( \frac { x } { 3 } = 42 \) . Multiply both sides by \( 3 \) . Kate's photo got \( 126 \) likes.
C. \( x + 3 = 42 \) . Subtract \( 3 \) from both sides. Kate's photo got \( 39 \) likes.
D. \( x - 3 = 42 \) . Add \( 3 \) to both sides. Kate's photo got \( 45 \) likes.
Ali's latest photo got \( 42 \) likes. This is \( 3 \) times as many likes as Kate's latest photo. How many likes did Kate's photo get? Select the correct solution method below, using \( x \) to represent Kate's likes.
A. \( 3 x = 42 \) . Divide both sides by \( 3 \) . Kate's photo got \( 14 \) likes.
B. \( \frac { x } { 3 } = 42 \) . Multiply both sides by \( 3 \) . Kate's photo got \( 126 \) likes.
C. \( x + 3 = 42 \) . Subtract \( 3 \) from both sides. Kate's photo got \( 39 \) likes.
D. \( x - 3 = 42 \) . Add \( 3 \) to both sides. Kate's photo got \( 45 \) likes.