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zimovet [89]
3 years ago
6

A new mixture of​ self-tanning & moisturizing lotions for everyday use is being developed. This mixture is made by mixing 70

0 ounces of everyday moisturizing lotion for ​$0.70 per ounce with​ self-tanning lotion worth ​$3 per ounce. If the new​ self-tanning & moisturizing lotion mixture is to cost $ 1.60 per​ ounce, how many ounces of the​ self-tanning lotion should be in the​ mixture?
Mathematics
1 answer:
777dan777 [17]3 years ago
7 0

Answer:

450 ounces

Step-by-step explanation:

We know that the cost of the mixture C_m must be the cost of the everyday moisturizing lotion C_e plus the cost of the self-tanning lotion C_s, which means C_m=C_e+C_s.

The cost of any substance will be the cost per ounce of the substance (c), multiplied by the number of ounces (n), which means C=nc, so we have from the previous formula that we have:

n_m c_m=n_e c_e + n_s c_s

But we also know that the number of ounces of the mixture must be the sum of the number of ounces of the everyday moisturizing lotion with the number of ounces of the self-tanning lotion, so we have

n_e c_e + n_s c_s=n_m c_m=(n_e+n_s) c_m=n_e c_m+n_s c_m

We want to calculate the number of ounces of the​ self-tanning lotion (n_s), so we solve for that variable:

n_e c_e + n_s c_s=n_e c_m+n_s c_m

n_s c_s-n_s c_m=n_e c_m-n_e c_e

n_s (c_s-c_m)=n_e(c_m-c_e)

n_s=\frac{n_e (c_m-c_e)}{(c_s-c_m)}

And substitute our values in this formula, to get:

n_s=\frac{(700\ ounces) (\$1.6-\$0.7)}{(\$3-\$1.6)}=450\ ounces

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Kipish [7]

Answer:

2.4 hours

Step-by-step explanation:

Let total work = X

Rate of work done = X ÷ time

Rate of A = X/4

Rate of B = X/6

If they work together, rate is the sum of their individual rates, i.e.

X/4 + X/6

= (3X + 2X)/12 (taking LCM)

=5X/12

Rate = X/time

5X/12 = X/time

time = X÷(5X/12)

time = X × 12/(5X)

time = 2.4 hours

Shortcut:

Product of individual times/sum of individual times

= (4×6)/(4+6)

=24/10

=2.4 hours

8 0
3 years ago
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Can someone help me for 20 points please? Thanks, make sure it is correct!
zzz [600]
Yes what do you need help with
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Abby, Bik, Cari, Dawn, and Ellen collect T-shirts. Abby has the most. Bik has 2.5 times as many T-shirts as Cari. Dawn has 1/3 a
bixtya [17]
A=abby's shirts
b=bik's shirts
c=cari's shirts
d=dawn's shirts
e=ellen's shirts


a> everybody
b=2.5c
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e=2d+1
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e=13=2d+1
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2 years ago
On the day of his 18th birthday harry decided to start saving money regularly
Veseljchak [2.6K]

We have been given that on the day of his 18th birthday Harry decided to start saving money regularly . Starting on that day, he could save 30.00 on the same date every month. We are asked to find the amount saved by the day before Harry's 60th birthday.

First of all, we will find years from 18 years to 60 years.

\text{Years}=60-18=42

We know that 1 year equals 12 months.

\text{42 years}=12\times 42\text{ Months}=504\text{ Months}

To find total amount saved, we will multiply 504 months by amount saved per month.

\text{Total amount saved}=\$30\times 504

\text{Total amount saved}=\$15,120

Therefore, Harry would have saved \$15,120 by the day before his 60th birthday.

3 0
3 years ago
Which of the following shapes have an area of 48 square feet? Select all that apply.
yKpoI14uk [10]
I think 2,3,4 or B,C,D would be correct.

The area of a triangle is (b•h)/2
And the area of a rectangle and parallelogram would just be b•h

1) 8(6) = 48/2 =24

2) 9(10 2/3) = 96/2 =48

3) 19.2(2.5) = 48

4) 16(3) = 48

Hope this is right and hope it helps. Have a good day
4 0
3 years ago
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