Question

20. Mr. Sprengel has a total amount of 91 pens and pencils. The ratio of pens to pencils is 6:7.
How many pencils does he have?

Answer 1

Answer:

Mr. Sprengel has 49 pencils.

Step-by-step explanation:

We are given that Mr. Sprengel has 91 pens and pencils.

We are also given that the ratio of pens to pencils is 6:7.

• We can create an equation to solve for how many pencils Mr. Sprengel has.

• In this case, our unknown variable is how many pencils Mr. Sprengel has.

Basically, the problem is telling us that for every 6 pens, there are 7 pencils.

Therefore, we can set up an equation and set our unknown (the amount of pencils) to be equal to x.

$\displaystyle6x + 7x = 91\\\\13x = 91\\\\x = 7$

Now, we found our x. However, we need to plug this into a new equation and find how many pens and pencils Mr. Sprengel has.

Our new equations are:

$\bullet \ 6(7) = y\\\\\bullet \ 7(7) = z$

In this case:

• y will equal the amount of pens.
• z will equal the amount of pencils.

Therefore, let's solve these:

$6(7) = y\\\\y = 42\\\\\\7(7) = z\\\\z = 49$

Now, finally, we need to insert these values into our newfound equation:

$\bullet \ y + z = 91$

$42 + 49 = 91\\\\91 = 91 \ \checkmark$

We get a true statement, so we have determined that Mr. Sprengel has:

• 42 pens
• 49 pencils