Emily is playing the video game Super Marlo Sisters. During her game, she
collects 8 boxes, each of which has either a coin (worth 100 points) or a flower
(worth 250 points). The total score from the 8 boxes is 1250 points. How many
of Emily’s boxes have flowers?

Question

UpStudy AI · Accepted Answer

To solve this problem, we can set up a system of equations based on the information given. Let's denote the number of boxes with coins as $$ c $$ and the number of boxes with flowers as $$ f $$.

Given:
1. The total number of boxes is 8, so $$ c + f = 8 $$.
2. The total score from the boxes is 1250 points. Since each coin is worth 100 points and each flower is worth 250 points, we can set up the equation $$ 100c + 250f = 1250 $$.

Now, we have a system of two equations:
1. $$ c + f = 8 $$
2. $$ 100c + 250f = 1250 $$

We can solve this system of equations to find the values of $$ c $$ and $$ f $$, which will tell us how many of Emily's boxes have flowers.
Solve the system of equations by following steps:
- step0: Solve using the substitution method:
  $$\left\{ \begin{array}{l}c+f=8\100c+250f=1250\end{array}ight.$$
- step1: Solve the equation:
  $$\left\{ \begin{array}{l}c=8-f\100c+250f=1250\end{array}ight.$$
- step2: Substitute the value of $$c:$$
  $$100\left(8-fight)+250f=1250$$
- step3: Simplify:
  $$800+150f=1250$$
- step4: Move the constant to the right side:
  $$150f=1250-800$$
- step5: Subtract the numbers:
  $$150f=450$$
- step6: Divide both sides:
  $$\frac{150f}{150}=\frac{450}{150}$$
- step7: Divide the numbers:
  $$f=3$$
- step8: Substitute the value of $$f:$$
  $$c=8-3$$
- step9: Simplify:
  $$c=5$$
- step10: Calculate:
  $$\left\{ \begin{array}{l}c=5\f=3\end{array}ight.$$
- step11: Check the solution:
  $$\left\{ \begin{array}{l}c=5\f=3\end{array}ight.$$
- step12: Rewrite:
  $$\left(c,fight) = \left(5,3ight)$$
The solution to the system of equations is $$ c = 5 $$ and $$ f = 3 $$.

Therefore, Emily has 3 boxes with flowers.
Emily has 3 boxes with flowers.

Emily is playing the video game Super Marlo Sisters. During her game, she
collects 8 boxes, each of which has either a coin (worth 100 points) or a flower
(worth 250 points). The total score from the 8 boxes is 1250 points. How many
of Emily’s boxes have flowers?

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Emily is playing the video game Super Marlo Sisters. During her game, she collects 8 boxes, each of which has either a coin (worth 100 points) or a flower (worth 250 points). The total score from the 8 boxes is 1250 points. How many of Emily’s boxes have flowers?

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Solución

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Emily is playing the video game Super Marlo Sisters. During her game, she
collects 8 boxes, each of which has either a coin (worth 100 points) or a flower
(worth 250 points). The total score from the 8 boxes is 1250 points. How many
of Emily’s boxes have flowers?