7) Two angles are supplementary. (Supplementary angles are angles whose sum is 1

Question

7) Two angles are supplementary. (Supplementary angles are angles whose sum is 180°.) Their difference is 22°. Find the angles.

8) Rick's Sporting Goods ran a promotion offering either a free rechargeable lantern or a free portable propane grill to each customer who bought a deluxe family tent. The store's cost for each lantern was $20, and its cost for each grill was $25. At the end of the promotion, 12 tents had been sold. The store's total cost for the items given away was $280. How many of each type of free item did the customers choose?

9) An executive nearing retirement made two investments totaling $45,000. In one year, these inestments yielded $2430 in simple interest. Part of the money was invested at 4% and the rest at 6%. How much was invested at each rate?

i need al 3 answers plz

Explanation / Answer

7)

If the measures are x and y degrees, and they are supplementary, then their sum is 180 degrees. So you can write and solve a system of equations.
x + y = 180
x - y = 22
Now you can use any method to solve. Let's use the elimination method by adding the equations together.
x + x + y - y = 180 + 22

2x = 222

x = 111
Now solve for y.
111 + y = 180
y = 69
So the angles measure 111 and 69 degrees.

8)

Let l = lanterns and g = grills

Since 12 tents were sold then l + g = 12
Also since the total cost of the giveaway items were $280 then 20l + 25g = 280

Solve the first equation for l: l = 12 - g

Now substitute 12 - g into the second equation for l so that you can solve for g.

20 (12 - g) + 25g = 280
240 - 20 g + 25g = 280 (distributive property)
240 + 5g = 280 (combining like terms)
5g = 40 (subtract 240 from both sides of the equal sign)
g = 8 ( divide both sides by 5)

Now substitute this value of g back into one of the equations:

l + g = 12
l + 8 = 12
l = 4

8 grills and 4 lanterns

9)

suppose x part invested in 4%

.04x+.06(45000-x)=2430
.04x+2700-.06x=2430
-.02x=-270

x=13500 at 4%
45000-x=31500 at 6%

so 13500 invested at 4%

and

31500 at 6%

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