write an equation that repersents the number of large baskets sold compared to small baskets
Your school Key club decided to sell baskets to raise money. The club sold a total of 80 baskets.
There are three different sized baskest. Small baskets sold for 15.75 dollars each. Medium baskets
sold for 25 dollars each. Large baskets sold for 32.50 each. The club took in a total of 2086.25
dollars, and they sold twice as many large baskets as small baskets.
x = large baskets sold
y = medium baskets sold
z = small baskets sold
x = 2z That is stated at the end of the problem. I can't believe that's
all that is required for this problem. Surely, the real intent is to find
out how many baskets of each size were sold.
x + y + z = 80
Prices: x --- 32.50 y --- 25.00 z --- 15.75
32.50x + 25.00y + 15.75z = 2086.25
Because we have x = 2z, we can substitute that into x + y + z = 80
2z + y + z = 80
y + 3z = 80
y = 80 - 3z
Substituting further:
32.50x + 25.00y + 15.75z = 2086.25
32.50(2z) + 25.00(80 - 3z) + 15.75z = 2086.25
Now, we have an equation with only one unknown. Solve it.
Multiply by 100 to eliminate the decimals.
100 * (32.50(2z) + 25.00(80 - 3z) + 15.75z) = 2086.25 * 100
3250(2z) + 2500(80 - 3z) + 1575z = 208625
6500z + 200000 - 7500z + 1575z = 208625
575z + 200000 = 208625
575z = 208625 - 200000
575z = 8625
z = 8625 / 575
z = 15 15 small baskets sold
We were told that there were twice as many large baskets sold.
x = 2z
x = 2 * 15
x = 30 30 large baskets sold
We were also told that a total of 80 baskets were sold.
x + y + z = 80
30 + y + 15 = 80
y + 45 = 80
y = 80 - 45
y = 35 35 medium baskets sold
Verify with the prices. Find out if the total income is correct.
32.50(30) + 25.00(35) + 15.75(15) = 2086.25
975.00 + 875.00 + 236.25 = 2086.25
2086.25 = 2086.25
It checks.